Expand all Collapse all | Results 1 - 25 of 89 |
1. CMB Online first
Approximate Fixed Point Sequences of Nonlinear Semigroup in Metric Spaces In this paper, we investigate the common
approximate fixed point sequences of nonexpansive semigroups of
nonlinear mappings $\{T_t\}_{t \geq 0}$, i.e., a family such that
$T_0(x)=x$, $T_{s+t}=T_s(T_t(x))$, where the domain is a metric space
$(M,d)$. In particular we prove that under suitable conditions, the
common approximate fixed point sequences set is the same as the common
approximate fixed point sequences set of two mappings from the family.
Then we use the Ishikawa iteration to construct a common approximate
fixed point sequence of nonexpansive semigroups of nonlinear
mappings.
Keywords:approximate fixed point, fixed point, hyperbolic metric space, Ishikawa iterations, nonexpansive mapping, semigroup of mappings, uniformly convex hyperbolic space Categories:47H09, 46B20, 47H10, 47E10 |
2. CMB Online first
Measures of Noncompactness in Regular Spaces Previous results by the author on the connection
between three of measures
of non-compactness obtained for $L_p$, are extended
to regular spaces of measurable
functions.
An example of advantage
in some cases one of them in comparison with another is given.
Geometric characteristics of regular spaces are determined.
New theorems for $(k,\beta)$-boundedness of partially additive
operators are proved.
Keywords:measure of non-compactness, condensing map, partially additive operator, regular space, ideal space Categories:47H08, 46E30, 47H99, 47G10 |
3. CMB Online first
New Characterizations of the Weighted Composition Operators Between Bloch Type Spaces in the Polydisk |
New Characterizations of the Weighted Composition Operators Between Bloch Type Spaces in the Polydisk We give some new characterizations for compactness of weighted
composition operators $uC_\varphi$ acting on Bloch-type spaces in
terms of the power of the components of $\varphi,$ where $\varphi$
is a holomorphic self-map of the polydisk $\mathbb{D}^n,$ thus
generalizing the results obtained by HyvÃ¤rinen and
LindstrÃ¶m in 2012.
Keywords:weighted composition operator, compactness, Bloch type spaces, polydisk, several complex variables Categories:47B38, 47B33, 32A37, 45P05, 47G10 |
4. CMB Online first
Constructive Proof of Carpenter's Theorem We give a constructive proof of Carpenter's Theorem due to Kadison.
Unlike the original proof our approach also yields the
real case of this theorem.
Keywords:diagonals of projections, the Schur-Horn theorem, the Pythagorean theorem, the Carpenter theorem, spectral theory Categories:42C15, 47B15, 46C05 |
5. CMB 2013 (vol 57 pp. 270)
Derivations on Toeplitz Algebras Let $H^2(\Omega)$ be the Hardy space on a strictly pseudoconvex domain $\Omega \subset
\mathbb{C}^n$,
and let $A \subset L^\infty(\partial \Omega)$ denote the subalgebra of all $L^\infty$-functions $f$
with compact Hankel operator $H_f$. Given any closed subalgebra $B \subset A$ containing $C(\partial \Omega)$,
we describe the first Hochschild cohomology group of the
corresponding Toeplitz algebra $\mathcal(B) \subset B(H^2(\Omega))$.
In particular, we show that every derivation on $\mathcal{T}(A)$ is inner. These results are new even for $n=1$,
where it follows that every derivation on $\mathcal{T}(H^\infty+C)$ is inner, while there are non-inner
derivations on $\mathcal{T}(H^\infty+C(\partial \mathbb{B}_n))$ over
the unit ball $\mathbb{B}_n$ in dimension $n\gt 1$.
Keywords:derivations, Toeplitz algebras, strictly pseudoconvex domains Categories:47B47, 47B35, 47L80 |
6. CMB 2012 (vol 57 pp. 166)
On Minimal and Maximal $p$-operator Space Structures We show that for $p$-operator spaces, there are natural notions of minimal and maximal
structures. These are useful for dealing with tensor products.
Keywords:$p$-operator space, min space, max space Categories:46L07, 47L25, 46G10 |
7. CMB 2012 (vol 57 pp. 80)
Semicrossed Products of the Disk Algebra and the Jacobson Radical We consider semicrossed products of the disk algebra with respect to
endomorphisms defined by finite Blaschke products. We characterize the Jacobson radical
of these operator algebras. Furthermore, in the case the finite Blaschke product is elliptic,
we show that the semicrossed product contains no nonzero quasinilpotent
elements. However, if the finite Blaschke product is hyperbolic or parabolic with positive hyperbolic step,
the Jacobson radical is nonzero and a proper subset of the set of quasinilpotent elements.
Keywords:semicrossed product, disk algebra, Jacobson radical Categories:47L65, 47L20, 30J10, 30H50 |
8. CMB 2012 (vol 56 pp. 477)
Hypercyclic Abelian Groups of Affine Maps on $\mathbb{C}^{n}$ We give a characterization of hypercyclic abelian group
$\mathcal{G}$ of affine maps on $\mathbb{C}^{n}$. If $\mathcal{G}$
is finitely generated, this characterization is explicit. We prove
in particular
that no abelian group generated by $n$ affine maps on $\mathbb{C}^{n}$ has a dense orbit.
Keywords:affine, hypercyclic, dense, orbit, affine group, abelian Categories:37C85, 47A16 |
9. CMB 2012 (vol 57 pp. 145)
The Essential Spectrum of the Essentially Isometric Operator Let $T$ be a contraction on a complex, separable, infinite dimensional
Hilbert space and let $\sigma \left( T\right) $ (resp. $\sigma _{e}\left(
T\right) )$ be its spectrum (resp. essential spectrum). We assume that $T$
is an essentially isometric operator, that is $I_{H}-T^{\ast }T$ is compact.
We show that if $D\diagdown \sigma \left( T\right) \neq \emptyset ,$ then
for every $f$ from the disc-algebra,
\begin{equation*}
\sigma _{e}\left( f\left( T\right) \right) =f\left( \sigma _{e}\left(
T\right) \right) ,
\end{equation*}
where $D$ is the open unit disc. In addition, if $T$ lies in the class
$ C_{0\cdot }\cup C_{\cdot 0},$ then
\begin{equation*}
\sigma _{e}\left( f\left( T\right) \right) =f\left( \sigma \left( T\right)
\cap \Gamma \right) ,
\end{equation*}
where $\Gamma $ is the unit circle. Some related problems are also discussed.
Keywords:Hilbert space, contraction, essentially isometric operator, (essential) spectrum, functional calculus Categories:47A10, 47A53, 47A60, 47B07 |
10. CMB 2012 (vol 57 pp. 25)
Subadditivity Inequalities for Compact Operators Some subadditivity inequalities for matrices and concave functions also hold for Hilbert space operators, but (unfortunately!) with an additional $\varepsilon$ term. It seems not possible to erase this residual term. However, in case of compact operators we show that the $\varepsilon$ term is unnecessary. Further, these inequalities are strict in a certain sense when some natural assumptions are satisfied. The discussion also stresses on matrices and their compressions and several open questions or conjectures are considered, both in the matrix and operator settings.
Keywords:concave or convex function, Hilbert space, unitary orbits, compact operators, compressions, matrix inequalities Categories:47A63, 15A45 |
11. CMB 2011 (vol 56 pp. 459)
On Certain Multivariable Subnormal Weighted Shifts and their Duals To every subnormal $m$-variable weighted shift $S$ (with bounded
positive weights) corresponds a positive Reinhardt measure $\mu$
supported on a compact Reinhardt subset of $\mathbb C^m$. We show that, for
$m \geq 2$, the dimensions of the $1$-st cohomology vector spaces
associated with the Koszul complexes of $S$ and its dual ${\tilde S}$
are different if a certain radial function happens to be integrable
with respect to $\mu$ (which is indeed the case with many classical
examples). In particular, $S$ cannot in that case be similar to
${\tilde S}$. We next prove that, for $m \geq 2$, a Fredholm subnormal
$m$-variable weighted shift $S$ cannot be similar to its dual.
Keywords:subnormal, Reinhardt, Betti numbers Category:47B20 |
12. CMB 2011 (vol 56 pp. 593)
On the $p$-norm of an Integral Operator in the Half Plane We give a partial answer to a conjecture of DostaniÄ on the
determination of the norm of a class of integral operators induced
by the weighted Bergman projection in the upper half plane.
Keywords:Bergman projection, integral operator, $L^p$-norm, the upper half plane Categories:47B38, 47G10, 32A36 |
13. CMB 2011 (vol 56 pp. 39)
Comparison Theorem for Conjugate Points of a Fourth-order Linear Differential Equation In 1961, J. Barrett showed that if the first conjugate point
$\eta_1(a)$ exists for the differential equation $(r(x)y'')''=
p(x)y,$ where $r(x)\gt 0$ and $p(x)\gt 0$, then so does the first
systems-conjugate point $\widehat\eta_1(a)$. The aim of this note is to
extend this result to the general equation with middle term
$(q(x)y')'$ without further restriction on $q(x)$, other than
continuity.
Keywords:fourth-order linear differential equation, conjugate points, system-conjugate points, subwronskians Categories:47E05, 34B05, 34C10 |
14. CMB 2011 (vol 56 pp. 400)
A Factorization Theorem for Multiplier Algebras of Reproducing Kernel Hilbert Spaces Let $(X,\mathcal B,\mu)$ be a $\sigma$-finite
measure space and let $H\subset L^2(X,\mu)$
be a separable reproducing kernel Hilbert
space on $X$. We show that the multiplier
algebra of $H$ has property $(A_1(1))$.
Keywords:reproducing kernel Hilbert space, Berezin transform, dual algebra Categories:46E22, 47B32, 47L45 |
15. CMB 2011 (vol 56 pp. 229)
CesÃ ro Operators on the Hardy Spaces of the Half-Plane In this article we study the CesÃ ro
operator
$$
\mathcal{C}(f)(z)=\frac{1}{z}\int_{0}^{z}f(\zeta)\,d\zeta,
$$
and its companion operator $\mathcal{T}$ on Hardy spaces of the
upper half plane. We identify $\mathcal{C}$ and $\mathcal{T}$ as
resolvents for appropriate semigroups of composition operators and we
find the norm and the spectrum in each case. The relation of
$\mathcal{C}$ and $\mathcal{T}$ with the corresponding Ces\`{a}ro
operators on Lebesgue spaces $L^p(\mathbb R)$ of the boundary line is also
discussed.
Keywords:CesÃ ro operators, Hardy spaces, semigroups, composition operators Categories:47B38, 30H10, 47D03 |
16. CMB 2011 (vol 55 pp. 646)
Marcinkiewicz Commutators with Lipschitz Functions in Non-homogeneous Spaces Under the assumption that $\mu$ is a nondoubling
measure, we study certain commutators generated by the
Lipschitz function and the Marcinkiewicz integral whose kernel
satisfies a HÃ¶rmander-type condition. We establish the boundedness
of these commutators on the Lebesgue spaces, Lipschitz spaces, and
Hardy spaces. Our results are extensions of known theorems in the
doubling case.
Keywords:non doubling measure, Marcinkiewicz integral, commutator, ${\rm Lip}_{\beta}(\mu)$, $H^1(\mu)$ Categories:42B25, 47B47, 42B20, 47A30 |
17. CMB 2011 (vol 55 pp. 673)
Multiplicity Free Jacquet Modules Let $F$ be a non-Archimedean local field or a finite field.
Let $n$ be a natural number and $k$ be $1$ or $2$.
Consider $G:=\operatorname{GL}_{n+k}(F)$ and let
$M:=\operatorname{GL}_n(F) \times \operatorname{GL}_k(F)\lt G$ be a maximal Levi subgroup.
Let $U\lt G$ be the corresponding unipotent subgroup and let $P=MU$ be the corresponding parabolic subgroup.
Let $J:=J_M^G: \mathcal{M}(G) \to \mathcal{M}(M)$ be the Jacquet functor, i.e., the functor of coinvariants with respect to $U$.
In this paper we prove that $J$ is a multiplicity free functor, i.e.,
$\dim \operatorname{Hom}_M(J(\pi),\rho)\leq 1$,
for any irreducible representations $\pi$ of $G$ and $\rho$ of $M$.
We adapt the classical method of Gelfand and Kazhdan, which proves the ``multiplicity free" property of certain representations to prove the ``multiplicity free" property of certain functors.
At the end we discuss whether other Jacquet functors are multiplicity free.
Keywords:multiplicity one, Gelfand pair, invariant distribution, finite group Categories:20G05, 20C30, 20C33, 46F10, 47A67 |
18. CMB 2011 (vol 55 pp. 555)
Weighted $L^p$ Boundedness of Pseudodifferential Operators and Applications In this paper we prove weighted norm inequalities with weights in
the $A_p$ classes, for pseudodifferential operators with symbols in
the class ${S^{n(\rho -1)}_{\rho, \delta}}$ that fall outside the
scope of CalderÃ³n-Zygmund theory. This is accomplished by
controlling the sharp function of the pseudodifferential operator by
Hardy-Littlewood type maximal functions. Our weighted norm
inequalities also yield $L^{p}$ boundedness of commutators of
functions of bounded mean oscillation with a wide class of operators
in $\mathrm{OP}S^{m}_{\rho, \delta}$.
Keywords:weighted norm inequality, pseudodifferential operator, commutator estimates Categories:42B20, 42B25, 35S05, 47G30 |
19. CMB 2011 (vol 54 pp. 654)
Norm One Idempotent $cb$-Multipliers with Applications to the Fourier Algebra in the $cb$-Multiplier Norm |
Norm One Idempotent $cb$-Multipliers with Applications to the Fourier Algebra in the $cb$-Multiplier Norm For a locally compact group $G$, let $A(G)$ be its Fourier algebra, let $M_{cb}A(G)$ denote the completely
bounded multipliers of $A(G)$, and let $A_{\mathit{Mcb}}(G)$ stand for the closure of $A(G)$ in $M_{cb}A(G)$. We
characterize the norm one idempotents in $M_{cb}A(G)$: the indicator function of a set $E \subset G$ is a norm
one idempotent in $M_{cb}A(G)$ if and only if $E$ is a coset of an open subgroup of $G$. As applications, we
describe the closed ideals of $A_{\mathit{Mcb}}(G)$ with an approximate identity bounded by $1$, and we characterize
those $G$ for which $A_{\mathit{Mcb}}(G)$ is $1$-amenable in the sense of B. E. Johnson. (We can even slightly
relax the norm bounds.)
Keywords:amenability, bounded approximate identity, $cb$-multiplier norm, Fourier algebra, norm one idempotent Categories:43A22, 20E05, 43A30, 46J10, 46J40, 46L07, 47L25 |
20. CMB 2011 (vol 54 pp. 456)
On Operator Sum and Product Adjoints and Closures We comment on domain conditions that regulate when the adjoint of the
sum or product of two unbounded operators is the sum or product of their
adjoints, and related closure issues. The quantum mechanical problem PHP
essentially selfadjoint for unbounded Hamiltonians is addressed, with new
results.
Keywords:unbounded operators, adjoints of sums and products, quantum mechanics Category:47A05 |
21. CMB 2011 (vol 55 pp. 15)
Browder's Convergence for One-Parameter Nonexpansive Semigroups We give the sufficient and necessary conditions
of Browder's convergence theorem
for one-parameter nonexpansive semigroups
which was proved by Suzuki.
We also discuss the perfect kernels of topological spaces.
Keywords:nonexpansive semigroup, common fixed point, Browder's convergence, perfect kernel Category:47H20 |
22. CMB 2011 (vol 55 pp. 882)
Equivalence of $L_p$ Stability and Exponential Stability of Nonlinear Lipschitzian Semigroups
$L_p$ stability and exponential stability are two important concepts
for nonlinear dynamic systems. In this paper, we prove that a
nonlinear exponentially bounded Lipschitzian semigroup is
exponentially stable if and only if the semigroup is $L_p$ stable
for some $p>0$. Based on the equivalence, we derive two sufficient
conditions for exponential stability of the nonlinear semigroup. The
results obtained extend and improve some existing ones.
Keywords:exponentially stable, $L_p$ stable, nonlinear Lipschitzian semigroups Categories:34D05, 47H20 |
23. CMB 2011 (vol 54 pp. 506)
On the Canonical Solution of the Sturm-Liouville Problem with Singularity and Turning Point of Even Order |
On the Canonical Solution of the Sturm-Liouville Problem with Singularity and Turning Point of Even Order In this paper, we are going to investigate the canonical property of solutions of
systems of differential equations having a singularity and turning
point of even order. First, by a replacement, we transform the system
to the Sturm-Liouville equation with turning point. Using of the
asymptotic estimates provided by Eberhard, Freiling, and Schneider
for a special fundamental system of solutions of the Sturm-Liouville
equation, we study the infinite product representation of solutions of the systems. Then we
transform the Sturm-Liouville equation with
turning point to the
equation with singularity, then we study the asymptotic behavior of its solutions. Such
representations are relevant to the inverse spectral problem.
Keywords:turning point, singularity, Sturm-Liouville, infinite products, Hadamard's theorem, eigenvalues Categories:34B05, 34Lxx, 47E05 |
24. CMB 2011 (vol 55 pp. 339)
From Matrix to Operator Inequalities We generalize LÃ¶wner's method for proving that matrix monotone
functions are operator monotone. The relation $x\leq y$ on bounded
operators is our model for a definition of $C^{*}$-relations
being residually finite dimensional.
Our main result is a meta-theorem about theorems involving relations
on bounded operators. If we can show there are residually finite dimensional
relations involved and verify a technical condition, then such a
theorem will follow from its restriction to matrices.
Applications are shown regarding norms of exponentials, the norms
of commutators, and "positive" noncommutative $*$-polynomials.
Keywords:$C*$-algebras, matrices, bounded operators, relations, operator norm, order, commutator, exponential, residually finite dimensional Categories:46L05, 47B99 |
25. CMB 2011 (vol 55 pp. 441)
Univalently Induced, Closed Range, Composition Operators on the Bloch-type Spaces While there is a large variety of univalently induced closed range
composition operators on the Bloch space,
we show that the only univalently induced, closed range, composition
operators on the Bloch-type spaces $B^{\alpha}$ with $\alpha \ne 1$
are the ones induced by a disc automorphism.
Keywords:composition operators, Bloch-type spaces, closed range, univalent Categories:47B35, 32A18 |