Expand all Collapse all | Results 1 - 25 of 70 |
1. CJM 2014 (vol 66 pp. 1110)
On the Dispersive Estimate for the Dirichlet SchrÃ¶dinger Propagator and Applications to Energy Critical NLS |
On the Dispersive Estimate for the Dirichlet SchrÃ¶dinger Propagator and Applications to Energy Critical NLS We consider the obstacle problem for the SchrÃ¶dinger evolution
in the exterior of the unit ball with Dirichlet boundary condition. Under
the radial symmetry we compute explicitly the fundamental solution
for the linear Dirichlet SchrÃ¶dinger
propagator $e^{it\Delta_D}$
and give a robust algorithm to prove sharp $L^1 \rightarrow
L^{\infty}$ dispersive estimates. We showcase the analysis in
dimensions $n=5,7$. As an application, we obtain global
well-posedness and scattering for defocusing energy-critical NLS on
$\Omega=\mathbb{R}^n\backslash \overline{B(0,1)}$ with Dirichlet boundary
condition and radial data in these dimensions.
Keywords:Dirichlet SchrÃ¶dinger propagator, dispersive estimate, Dirichlet boundary condition, scattering theory, energy critical Categories:35P25, 35Q55, 47J35 |
2. CJM 2013 (vol 67 pp. 132)
Unitary Equivalence and Similarity to Jordan Models for Weak Contractions of Class $C_0$ We obtain results on the unitary equivalence of weak contractions of
class $C_0$ to their Jordan models under an assumption on their
commutants. In particular, our work addresses the case of arbitrary
finite multiplicity. The main tool is the
theory of boundary representations due to Arveson. We also
generalize and improve previously known results concerning unitary
equivalence and similarity to Jordan models when the minimal function
is a Blaschke product.
Keywords:weak contractions, operators of class $C_0$, Jordan model, unitary equivalence Categories:47A45, 47L55 |
3. CJM 2013 (vol 66 pp. 1143)
Maps Preserving Complementarity of Closed Subspaces of a Hilbert Space Let $\mathcal{H}$ and $\mathcal{K}$ be infinite-dimensional separable
Hilbert spaces and ${\rm Lat}\,\mathcal{H}$ the lattice of all closed subspaces oh $\mathcal{H}$.
We describe the general form of pairs of bijective maps $\phi , \psi :
{\rm Lat}\,\mathcal{H} \to {\rm Lat}\,\mathcal{K}$ having the property that for every pair
$U,V \in {\rm Lat}\,\mathcal{H}$ we have $\mathcal{H} = U \oplus V \iff \mathcal{K} = \phi (U) \oplus \psi (V)$. Then we reformulate this theorem as a description
of bijective image equality and kernel equality preserving maps acting on bounded linear idempotent operators. Several known
structural results for maps on idempotents are easy consequences.
Keywords:Hilbert space, lattice of closed subspaces, complemented subspaces, adjacent subspaces, idempotents Categories:46B20, 47B49 |
4. CJM 2013 (vol 65 pp. 1005)
Uniformly Continuous Functionals and M-Weakly Amenable Groups Let $G$ be a locally compact group. Let $A_{M}(G)$ ($A_{0}(G)$)denote
the closure of $A(G)$, the Fourier algebra of $G$ in the space of
bounded (completely bounded) multipliers of $A(G)$.
We call a locally compact group M-weakly amenable if
$A_M(G)$
has a
bounded approximate identity. We will show that when $G$ is M-weakly
amenable, the algebras $A_{M}(G)$ and $A_{0}(G)$ have
properties that are characteristic of the Fourier algebra of an
amenable group. Along the way we show that the sets of tolopolically
invariant means associated with these algebras have the same
cardinality as those of the Fourier algebra.
Keywords:Fourier algebra, multipliers, weakly amenable, uniformly continuous functionals Categories:43A07, 43A22, 46J10, 47L25 |
5. CJM 2013 (vol 66 pp. 387)
Composition of Inner Functions We study the image of the model subspace $K_\theta$ under the
composition operator $C_\varphi$, where $\varphi$ and $\theta$ are
inner functions, and find the smallest model subspace which contains
the linear manifold $C_\varphi K_\theta$. Then we characterize the
case when $C_\varphi$ maps $K_\theta$ into itself. This case leads to
the study of the inner functions $\varphi$ and $\psi$ such that the
composition $\psi\circ\varphi$ is a divisor of $\psi$ in the family of
inner functions.
Keywords:composition operators, inner functions, Blaschke products, model subspaces Categories:30D55, 30D05, 47B33 |
6. CJM 2013 (vol 65 pp. 783)
Generalised Triple Homomorphisms and Derivations We introduce generalised triple homomorphism between Jordan Banach
triple systems as a concept which extends the notion of generalised homomorphism between
Banach algebras given by K. Jarosz and B.E. Johnson in 1985 and 1987, respectively.
We prove that every generalised triple homomorphism between JB$^*$-triples
is automatically continuous. When particularised to C$^*$-algebras, we rediscover
one of the main theorems established by B.E. Johnson. We shall also consider generalised
triple derivations from a Jordan Banach triple $E$ into a Jordan Banach triple $E$-module,
proving that every generalised triple derivation from a JB$^*$-triple $E$ into itself or into $E^*$
is automatically continuous.
Keywords:generalised homomorphism, generalised triple homomorphism, generalised triple derivation, Banach algebra, Jordan Banach triple, C$^*$-algebra, JB$^*$-triple Categories:46L05, 46L70, 47B48, 17C65, 46K70, 46L40, 47B47, 47B49 |
7. CJM 2013 (vol 66 pp. 641)
Heat Kernels and Green Functions on Metric Measure Spaces We prove that, in a setting of local Dirichlet forms on metric measure
spaces, a two-sided sub-Gaussian estimate of the heat kernel is equivalent
to the conjunction of the volume doubling propety, the elliptic Harnack
inequality and a certain estimate of the capacity between concentric balls.
The main technical tool is the equivalence between the capacity estimate and
the estimate of a mean exit time in a ball, that uses two-sided estimates of
a Green function in a ball.
Keywords:Dirichlet form, heat kernel, Green function, capacity Categories:35K08, 28A80, 31B05, 35J08, 46E35, 47D07 |
8. CJM 2012 (vol 65 pp. 768)
Nonself-adjoint Semicrossed Products by Abelian Semigroups Let $\mathcal{S}$ be the semigroup $\mathcal{S}=\sum^{\oplus k}_{i=1}\mathcal{S}_i$, where for each $i\in I$,
$\mathcal{S}_i$ is a countable subsemigroup of the additive semigroup $\mathbb{R}_+$ containing $0$. We consider representations
of $\mathcal{S}$ as contractions $\{T_s\}_{s\in\mathcal{S}}$ on a Hilbert space with the Nica-covariance property:
$T_s^*T_t=T_tT_s^*$ whenever $t\wedge s=0$. We show that all such representations have a unique minimal isometric Nica-covariant
dilation.
This result is used to help analyse the nonself-adjoint semicrossed product algebras formed from Nica-covariant representations of the action of $\mathcal{S}$ on an operator algebra $\mathcal{A}$ by completely contractive endomorphisms.
We conclude by calculating the $C^*$-envelope of the isometric nonself-adjoint semicrossed product algebra (in the sense
of Kakariadis and Katsoulis).
Keywords:semicrossed product, crossed product, C*-envelope, dilations Categories:47L55, 47A20, 47L65 |
9. CJM 2011 (vol 64 pp. 1329)
Composition Operators Induced by Analytic Maps to the Polydisk We study properties of composition operators
induced by symbols acting from the unit disk to the polydisk.
This result will be involved in the investigation
of weighted composition operators on the Hardy space on the unit disk
and moreover be concerned with composition operators acting
from the Bergman space to the Hardy space on the unit disk.
Keywords:composition operators, Hardy spaces, polydisk Categories:47B33, 32A35, 30H10 |
10. CJM 2011 (vol 63 pp. 1161)
Transfer of Fourier Multipliers into Schur Multipliers and Sumsets in a Discrete Group We inspect the relationship between relative Fourier
multipliers on noncommutative Lebesgue-Orlicz spaces of a discrete
group $\varGamma$ and relative Toeplitz-Schur multipliers on
Schatten-von-Neumann-Orlicz classes. Four applications are given:
lacunary sets, unconditional Schauder bases for the subspace of a
Lebesgue space determined by a given spectrum $\varLambda\subseteq\varGamma$, the
norm of the Hilbert transform and the Riesz projection on
Schatten-von-Neumann classes with exponent a power of 2, and the norm of
Toeplitz Schur multipliers on Schatten-von-Neumann classes with
exponent less than 1.
Keywords:Fourier multiplier, Toeplitz Schur multiplier, lacunary set, unconditional approximation property, Hilbert transform, Riesz projection Categories:47B49, 43A22, 43A46, 46B28 |
11. CJM 2011 (vol 64 pp. 183)
Negative Powers of Laguerre Operators We study negative powers of Laguerre differential operators in $\mathbb{R}^d$, $d\ge1$.
For these operators we prove two-weight $L^p-L^q$ estimates with ranges of $q$ depending
on $p$. The case of the harmonic oscillator (Hermite operator) has recently
been treated by Bongioanni and Torrea by using a straightforward
approach of kernel estimates. Here these results are applied in certain Laguerre settings.
The procedure is fairly direct for Laguerre function expansions of
Hermite type,
due to some monotonicity properties of the kernels involved.
The case of Laguerre function expansions of convolution type is less straightforward.
For half-integer type indices $\alpha$ we transfer the desired results from the Hermite setting
and then apply an interpolation argument based on a device we call the
Keywords:potential operator, fractional integral, Riesz potential, negative power, harmonic oscillator, Laguerre operator, Dunkl harmonic oscillator Categories:47G40, 31C15, 26A33 |
12. CJM 2011 (vol 63 pp. 1188)
On Complemented Subspaces of Non-Archimedean Power Series Spaces The non-archimedean power series spaces, $A_1(a)$ and $A_\infty(b)$, are the
best known and most important examples of non-archimedean nuclear FrÃ©chet spaces.
We prove that the range of every continuous linear map from $A_p(a)$ to $A_q(b)$
has a Schauder basis if either $p=1$ or $p=\infty$ and the set $M_{b,a}$ of all
bounded limit points of the double sequence
$(b_i/a_j)_{i,j\in\mathbb{N}}$ is bounded. It
follows that every complemented subspace of a power series space $A_p(a)$ has a
Schauder basis if either $p=1$ or $p=\infty$ and the set $M_{a,a}$ is bounded.
Keywords:non-archimedean KÃ¶the space, range of a continuous linear map, Schauder basis Categories:46S10, 47S10, 46A35 |
13. CJM 2011 (vol 63 pp. 862)
Linear Combinations of Composition Operators on the Bloch Spaces We characterize the compactness of linear combinations of analytic
composition operators on the Bloch space. We also study
their boundedness and compactness on the little Bloch space.
Keywords: composition operator, compactness, Bloch space Categories:47B33, 30D45, 47B07 |
14. CJM 2011 (vol 63 pp. 648)
Spectral Asymptotics of Laplacians Associated with One-dimensional Iterated Function Systems with Overlaps |
Spectral Asymptotics of Laplacians Associated with One-dimensional Iterated Function Systems with Overlaps We set up a framework for computing the spectral dimension of a class of one-dimensional
self-similar measures that are defined by iterated function systems
with overlaps and satisfy a family of second-order self-similar
identities. As applications of our result we obtain the spectral dimension
of important measures such as the infinite Bernoulli convolution
associated with the golden ratio and convolutions of Cantor-type measures.
The main novelty of our result is that the iterated function systems
we consider are not post-critically finite and do not satisfy the
well-known open set condition.
Keywords:spectral dimension, fractal, Laplacian, self-similar measure, iterated function system with overlaps, second-order self-similar identities Categories:28A80, , , , 35P20, 35J05, 43A05, 47A75 |
15. CJM 2011 (vol 63 pp. 533)
On Best Proximity Points in Metric and Banach Spaces In this paper we study the existence and uniqueness of
best proximity points of cyclic contractions as well as the convergence
of iterates to such proximity points. We take two different approaches,
each one leading to different results that complete, if not improve,
other similar results in the theory. Results in this paper stand for Banach
spaces, geodesic metric spaces and metric spaces. We also include an appendix
on CAT$(0)$ spaces where we study the particular behavior of these spaces
regarding the problems we are concerned with.
Categories:54H25, 47H09 |
16. CJM 2010 (vol 62 pp. 1419)
BMO-Estimates for Maximal Operators via Approximations of the Identity with Non-Doubling Measures
Let $\mu$ be a nonnegative Radon measure
on $\mathbb{R}^d$ that satisfies the growth condition that there exist
constants $C_0>0$ and $n\in(0,d]$ such that for all $x\in\mathbb{R}^d$ and
$r>0$, ${\mu(B(x,\,r))\le C_0r^n}$, where $B(x,r)$ is the open ball
centered at $x$ and having radius $r$. In this paper, the authors prove
that if $f$ belongs to the $\textrm {BMO}$-type space $\textrm{RBMO}(\mu)$ of Tolsa, then
the homogeneous maximal function $\dot{\mathcal{M}}_S(f)$ (when $\mathbb{R}^d$ is not an
initial cube) and the inhomogeneous maximal function
$\mathcal{M}_S(f)$ (when $\mathbb{R}^d$ is an initial cube)
associated with a given approximation of the identity $S$ of Tolsa are
either infinite everywhere or finite almost everywhere,
and in the latter case, $\dot{\mathcal{M}}_S$ and $\mathcal{M}_S$ are bounded from
$\textrm{RBMO}(\mu)$ to the $\textrm {BLO}$-type
space $\textrm{RBLO}(\mu)$. The authors also prove that the inhomogeneous
maximal operator $\mathcal{M}_S$ is bounded from the local
$\textrm {BMO}$-type space $\textrm{rbmo}(\mu)$
to the local $\textrm {BLO}$-type space $\textrm{rblo}(\mu)$.
Keywords:Non-doubling measure, maximal operator, approximation of the identity, RBMO(mu), RBLO(mu), rbmo(mu), rblo(mu) Categories:42B25, 42B30, 47A30, 43A99 |
17. CJM 2010 (vol 62 pp. 889)
Singular Integral Operators and Essential Commutativity on the Sphere Let ${\mathcal T}$ be the $C^\ast $-algebra generated by the Toeplitz operators $\{T_\varphi : \varphi \in L^\infty (S,d\sigma )\}$ on the Hardy space $H^2(S)$ of the unit sphere in $\mathbf{C}^n$. It is well known that ${\mathcal T}$ is contained in the essential commutant of $\{T_\varphi : \varphi \in \operatorname{VMO}\cap L^\infty (S,d\sigma )\}$. We show that the essential commutant of $\{T_\varphi : \varphi \in \operatorname{VMO}\cap L^\infty (S,d\sigma )\}$ is strictly larger than ${\mathcal T}$.
Categories:32A55, 46L05, 47L80 |
18. CJM 2009 (vol 62 pp. 74)
Projectors on the Generalized Eigenspaces for Neutral Functional Differential Equations in $L^{p}$ Spaces |
Projectors on the Generalized Eigenspaces for Neutral Functional Differential Equations in $L^{p}$ Spaces We present the explicit formulas for the projectors on the generalized
eigenspaces associated with some eigenvalues for linear neutral functional
differential equations (NFDE) in $L^{p}$ spaces by using integrated
semigroup theory. The analysis is based on the main result
established elsewhere by the authors and results by Magal and Ruan
on non-densely defined Cauchy problem.
We formulate the NFDE as a non-densely defined Cauchy problem and obtain
some spectral properties from which we then derive explicit formulas for
the projectors on the generalized eigenspaces associated with some
eigenvalues. Such explicit formulas are important in studying bifurcations
in some semi-linear problems.
Keywords:neutral functional differential equations, semi-linear problem, integrated semigroup, spectrum, projectors Categories:34K05, 35K57, 47A56, 47H20 |
19. CJM 2009 (vol 62 pp. 415)
Classification of Reducing Subspaces of a Class of Multiplication Operators on the Bergman Space via the Hardy Space of the Bidisk |
Classification of Reducing Subspaces of a Class of Multiplication Operators on the Bergman Space via the Hardy Space of the Bidisk In this paper we obtain a complete description of nontrivial minimal reducing subspaces of the multiplication operator by a Blaschke product with four zeros on the Bergman space of the unit disk via the Hardy space of the bidisk.
Categories:47B35, 47B38 |
20. CJM 2009 (vol 62 pp. 439)
On Hankel Forms of Higher Weights: The Case of Hardy Spaces In this paper we study bilinear Hankel forms of higher weights on Hardy spaces in several dimensions. (The Schatten class Hankel forms of higher weights on weighted Bergman spaces have already been studied by Janson and Peetre for one dimension and by SundhÃ¤ll for several dimensions). We get a full characterization of Schatten class Hankel forms in terms of conditions for the symbols to be in certain Besov spaces. Also, the Hankel forms are bounded and compact if and only if the symbols satisfy certain Carleson measure criteria and vanishing Carleson measure criteria, respectively.
Keywords:Hankel forms, Schattenâvon Neumann classes, Bergman spaces, Hardy spaces, Besov spaces, transvectant, unitary representations, MÃ¶bius group Categories:32A25, 32A35, 32A37, 47B35 |
21. CJM 2009 (vol 62 pp. 305)
Approximation and Similarity Classification of Stably Finitely Strongly Irreducible Decomposable Operators |
Approximation and Similarity Classification of Stably Finitely Strongly Irreducible Decomposable Operators Let $\mathcal H$ be a complex separable Hilbert space and ${\mathcal L}({\mathcal H})$ denote the collection of bounded linear operators on ${\mathcal H}$. In this paper, we show that for any operator $A\in{\mathcal L}({\mathcal H})$, there exists a stably finitely (SI) decomposable operator $A_\epsilon$, such that $\|A-A_{\epsilon}\|<\epsilon$ and ${\mathcal{\mathcal A}'(A_{\epsilon})}/\operatorname{rad} {{\mathcal A}'(A_{\epsilon})}$ is commutative, where $\operatorname{rad}{{\mathcal A}'(A_{\epsilon})}$ is the Jacobson radical of ${{\mathcal A}'(A_{\epsilon})}$. Moreover, we give a similarity classification of the stably finitely decomposable operators that generalizes the result on similarity classification of Cowen-Douglas operators given by C. L. Jiang.
Keywords:$K_{0}$-group, strongly irreducible decomposition, CowenâDouglas operators, commutant algebra, similarity classification Categories:47A05, 47A55, 46H20 |
22. CJM 2009 (vol 62 pp. 242)
A Second Order Smooth Variational Principle on Riemannian Manifolds We establish a second order smooth variational principle valid for functions defined on (possibly infinite-dimensional) Riemannian manifolds which are uniformly locally convex and have a strictly positive injectivity radius and bounded sectional curvature.
Keywords:smooth variational principle, Riemannian manifold Categories:58E30, 49J52, 46T05, 47J30, 58B20 |
23. CJM 2009 (vol 62 pp. 133)
Some Applications of the Perturbation Determinant in Finite von Neumann Algebras In the finite von Neumann algebra setting, we introduce the concept
of a perturbation determinant associated with a pair of self-adjoint
elements $H_0$ and $H$ in the algebra and relate it to the concept of
the de la Harpe--Skandalis homotopy invariant determinant associated
with piecewise $C^1$-paths of operators joining $H_0$ and $H$. We
obtain an analog of Krein's formula that relates the perturbation
determinant and the spectral shift function and, based on this
relation, we derive subsequently (i) the Birman--Solomyak formula for
a general non-linear perturbation, (ii) a universality of a spectral
averaging, and (iii) a generalization of the
Dixmier--Fuglede--Kadison differentiation formula.
Keywords:perturbation determinant, trace formulae, von Neumann algebras Categories:47A55, 47C15, 47A53 |
24. CJM 2009 (vol 61 pp. 1239)
Periodicity in Rank 2 Graph Algebras Kumjian and Pask introduced an aperiodicity condition
for higher rank graphs.
We present a detailed analysis of when this occurs
in certain rank 2 graphs.
When the algebra is aperiodic, we give another proof
of the simplicity of $\mathrm{C}^*(\mathbb{F}^+_{\theta})$.
The periodic $\mathrm{C}^*$-algebras are characterized, and it is shown
that $\mathrm{C}^*(\mathbb{F}^+_{\theta}) \simeq
\mathrm{C}(\mathbb{T})\otimes\mathfrak{A}$
where $\mathfrak{A}$ is a simple $\mathrm{C}^*$-algebra.
Keywords:higher rank graph, aperiodicity condition, simple $\mathrm{C}^*$-algebra, expectation Categories:47L55, 47L30, 47L75, 46L05 |
25. CJM 2009 (vol 61 pp. 282)
Closed Ideals in Some Algebras of Analytic Functions We obtain a complete description of closed ideals of the algebra
$\cD\cap \cL$, $0<\alpha\leq\frac{1}{2}$, where $\cD$ is the
Dirichlet space and $\cL$ is the algebra of analytic functions
satisfying the Lipschitz condition of order $\alpha$.
Categories:46E20, 30H05, 47A15 |