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Results 26 - 50 of 85 |
26. CMB 2010 (vol 54 pp. 364)
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Lyapunov Theorems for the Asymptotic Behavior of Evolution Families on the Half-Line
Two theorems regarding the
asymptotic behavior of evolution families are established in
terms of the solutions of a certain Lyapunov operator equation.
Keywords:evolution families, exponential instability, Lyapunov equation Categories:34D05, 47D06 |
27. CMB 2010 (vol 54 pp. 21)
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Generalized D-symmetric Operators II
Let $H$ be a separable,
infinite-dimensional, complex Hilbert space and let $A, B\in{\mathcal L
}(H)$, where ${\mathcal L}(H)$ is the algebra of all bounded linear
operators on $H$. Let $\delta_{AB}\colon {\mathcal L}(H)\rightarrow {\mathcal
L}(H)$ denote the generalized derivation $\delta_{AB}(X)=AX-XB$.
This note will initiate a study on the class of pairs $(A,B)$ such
that $\overline{{\mathcal R}(\delta_{AB})}= \overline{{\mathcal
R}(\delta_{A^{\ast}B^{\ast}})}$.
Keywords:generalized derivation, adjoint, D-symmetric operator, normal operator Categories:47B47, 47B10, 47A30 |
28. CMB 2010 (vol 54 pp. 28)
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Generalized Solution of the Photon Transport Problem
The purpose of this paper is to show the existence of a
generalized solution of the photon transport problem. By means of the theory of
equicontinuous $C_{0}$-semigroup on a sequentially complete locally convex
topological vector space we show that the perturbed abstract Cauchy problem
has a unique solution when the perturbation operator and the forcing term
function satisfy certain conditions. A consequence of the abstract result is
that it can be directly applied to obtain a generalized solution of the photon
transport problem.
Keywords:photon transport, $C_{0}$-semigroup Categories:35K30, 47D03 |
29. CMB 2010 (vol 54 pp. 3)
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Extensions of Positive Definite Functions on Amenable Groups
Let $S$ be a subset of an amenable group $G$ such that $e\in S$ and
$S^{-1}=S$. The main result of this paper states that if the Cayley
graph of $G$ with respect to $S$ has a certain combinatorial property,
then every positive definite operator-valued function on $S$ can be
extended to a positive definite function on $G$. Several known
extension results are obtained as corollaries. New applications are
also presented.
Categories:43A35, 47A57, 20E05 |
30. CMB 2010 (vol 54 pp. 141)
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Linear Maps on $C^*$-Algebras Preserving the Set of Operators that are Invertible in $\mathcal{A}/\mathcal{I}$
For $C^*$-algebras $\mathcal{A}$ of real rank zero, we describe
linear maps $\phi$ on $\mathcal{A}$ that are surjective up to ideals
$\mathcal{I}$, and $\pi(A)$ is invertible in $\mathcal{A}/\mathcal{I}$ if and only if
$\pi(\phi(A))$ is invertible in $\mathcal{A}/\mathcal{I}$, where $A\in\mathcal{A}$ and
$\pi:\mathcal{A}\to\mathcal{A}/\mathcal{I}$ is the quotient map. We also consider similar
linear maps preserving zero products on the Calkin algebra.
Keywords:preservers, Jordan automorphisms, invertible operators, zero products Categories:47B48, 47A10, 46H10 |
31. CMB 2010 (vol 53 pp. 550)
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Representing a Product System Representation as a Contractive Semigroup and Applications to Regular Isometric Dilations
In this paper we propose a new technical tool for analyzing
representations of Hilbert $C^*$-product systems. Using this tool,
we give a new proof that every doubly commuting representation
over $\mathbb{N}^k$ has a regular isometric dilation, and we also
prove sufficient conditions for the existence of a regular
isometric dilation of representations over more general
subsemigroups of $\mathbb R_{+}^k$.
Categories:47A20, 46L08 |
32. CMB 2010 (vol 53 pp. 398)
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Projections in the Convex Hull of Surjective Isometries We characterize those linear projections represented as a convex combination of two surjective isometries on standard Banach spaces of continuous functions with values in a strictly convex Banach space.
Keywords:isometry, convex combination of isometries, generalized bi-circular projections Categories:47A65, 47B15, 47B37 |
33. CMB 2010 (vol 53 pp. 466)
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Separating Maps between Spaces of Vector-Valued Absolutely Continuous Functions In this paper we give a description of separating or disjointness preserving linear bijections on spaces of vector-valued absolutely continuous functions defined on compact subsets of the real line. We obtain that they are continuous and biseparating in the finite-dimensional case. The infinite-dimensional case is also studied.
Keywords:separating maps, disjointness preserving, vector-valued absolutely continuous functions, automatic continuity Categories:47B38, 46E15, 46E40, 46H40, 47B33 |
34. CMB 2008 (vol 51 pp. 604)
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The Invariant Subspace Problem for Non-Archimedean Banach Spaces It is proved that every infinite-dimensional
non-archimedean Banach space of countable type admits a linear
continuous operator without a non-trivial closed invariant
subspace. This solves a problem stated by A.~C.~M. van Rooij and
W.~H. Schikhof in 1992.
Keywords:invariant subspaces, non-archimedean Banach spaces Categories:47S10, 46S10, 47A15 |
35. CMB 2008 (vol 51 pp. 481)
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Universal Inner Functions on the Ball It is shown that given any sequence of automorphisms $(\phi_k)_k$ of the
unit ball $\bn$ of $\cn$ such that $\|\phi_k(0)\|$ tends to $1$,
there exists an inner function
$I$ such that the family of ``non-Euclidean translates"
$(I\circ\phi_k)_k$ is locally uniformly dense in the unit ball of
$H^\infty(\bn)$.
Keywords:inner functions, automorphisms of the ball, universality Categories:32A35, 30D50, 47B38 |
36. CMB 2008 (vol 51 pp. 372)
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Picard's Iterations for Integral Equations of Mixed Hammerstein Type A new semilocal convergence result for the Picard method is presented,
where the main required condition in the contraction mapping principle is relaxed.
Keywords:nonlinear equations in Banach spaces, successive approximations, semilocal convergence theorem, Picard's iteration, Hammerstein integral equations Categories:45G10, 47H99, 65J15 |
37. CMB 2008 (vol 51 pp. 378)
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Cyclic Vectors in Some Weighted $L^p$ Spaces of Entire Functions In this paper,
we generalize a result recently obtained by the author.
We characterize the cyclic vectors in $\Lp$.
Let $f\in\Lp$ and $f\poly$ be contained in the space.
We show that $f$ is non-vanishing if and only if $f$ is cyclic.
Keywords:weighted $L^p$ spaces of entire functions, cyclic vectors Categories:47A16, 46J15, 46H25 |
38. CMB 2008 (vol 51 pp. 67)
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Rearrangement-Invariant Functionals with Applications to Traces on Symmetrically Normed Ideals We present a construction of singular rearrangement
invariant functionals on Marcinkiewicz function/operator spaces.
The functionals constructed differ from all previous examples in
the literature in that they fail to be symmetric. In other words,
the functional $\phi$ fails the condition that if $x\pprec y$
(Hardy-Littlewood-Polya submajorization) and $0\leq x,y$, then
$0\le \phi(x)\le \phi(y).$ We apply our results to singular traces
on symmetric operator spaces (in particular on
symmetrically-normed ideals of compact operators), answering
questions raised by Guido and Isola.
Categories:46L52, 47B10, 46E30 |
39. CMB 2007 (vol 50 pp. 172)
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An Infinite Dimensional Vector Space of Universal Functions for $H^\infty$ of the Ball We show that there exists a closed infinite dimensional subspace
of $H^\infty(B^n)$ such that every function of norm one is
universal for some sequence of automorphisms of $B^n$.
Categories:47B38, 47B33, 46J10 |
40. CMB 2007 (vol 50 pp. 85)
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Classification of Finite Group-Frames and Super-Frames Given a finite group $G$, we examine the classification of all
frame representations of $G$ and the classification of all
$G$-frames, \emph{i.e.,} frames induced by group representations of $G$.
We show that the exact number of equivalence classes of $G$-frames
and the exact number of frame representations can be explicitly
calculated. We also discuss how to calculate the largest number
$L$ such that there exists an $L$-tuple of strongly disjoint
$G$-frames.
Keywords:frames, group-frames, frame representations, disjoint frames Categories:42C15, 46C05, 47B10 |
41. CMB 2006 (vol 49 pp. 117)
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A Double Triangle Operator Algebra From $SL_2(\R)$ We consider the w$^*$-closed operator algebra $\cA_+$ generated
by the image of the semigroup $SL_2(\R_+)$ under a unitary representation
$\rho$ of $SL_2(\R)$ on the Hilbert~space $L_2(\R)$.
We show that $\cA_+$ is a reflexive operator algebra and
$\cA_+=\Alg\cD$ where $\cD$ is a double triangle subspace
lattice. Surprisingly, $\cA_+$ is also generated as a
w$^*$-closed algebra by the image under $\rho$ of a strict
subsemigroup of $SL_2(\R_+)$.
Categories:46K50, 47L55 |
42. CMB 2005 (vol 48 pp. 607)
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Toeplitz Algebras and Extensions of\\Irrational Rotation Algebras For a given irrational number $\theta$, we define Toeplitz operators with
symbols in the irrational rotation algebra ${\mathcal A}_\theta$,
and we show that the $C^*$-algebra $\mathcal T({\mathcal
A}_\theta)$ generated by these Toeplitz operators is an extension
of ${\mathcal A}_\theta$ by the algebra of compact operators. We
then use these extensions to explicitly exhibit generators of the
group $KK^1({\mathcal A}_\theta,\mathbb C)$. We also prove an
index theorem for $\mathcal T({\mathcal A}_\theta)$ that
generalizes the standard index theorem for Toeplitz operators on
the circle.
Keywords:Toeplitz operators, irrational rotation algebras, index theory Categories:47B35, 46L80 |
43. CMB 2005 (vol 48 pp. 409)
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The Existence of Universal Inner Functions on the Unit Ball of $\mathbb{C}^n$ It is shown that there exists an inner function
$I$ defined on the unit ball ${\bf B}^n$ of ${\mathbb C}^n$
such that each function holomorphic on ${\bf B}^n$ and
bounded by $1$ can be approximated by
``non-Euclidean translates" of $I$.
Keywords:universal inner functions Categories:32A35, 30D50, 47B38 |
44. CMB 2005 (vol 48 pp. 251)
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The Index Theory Associated to a Non-Finite Trace on a $C^\ast$-Algebra The index theory considered in this paper, a
generalisation of the classical Fredholm index theory, is obtained
in terms of a non-finite trace on a unital $C^\ast$-algebra. We relate
it to the index theory of M.~Breuer, which is developed in a
von~Neumann algebra setting, by means of a representation theorem.
We show how our new index theory can be used to obtain an index
theorem for Toeplitz operators on the compact group $\mathbf{U}(2)$,
where the classical index theory does not give any interesting result.
Categories:46L, 47B35, 47L80 |
45. CMB 2005 (vol 48 pp. 97)
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On the Ranges of Bimodule Projections We develop a symbol calculus for normal bimodule maps over a masa
that is the natural analogue of the Schur product theory. Using
this calculus we are easily able to give a complete description of
the ranges of contractive normal bimodule idempotents that avoids
the theory of J*-algebras.
We prove that if $P$ is a normal
bimodule idempotent and $\|P\| < 2/\sqrt{3}$ then $P$ is a
contraction. We finish with some attempts at extending the symbol
calculus to non-normal maps.
Categories:46L15, 47L25 |
46. CMB 2004 (vol 47 pp. 615)
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$C^*$-Algebras and Factorization Through Diagonal Operators Let $\cal A$ be a $C^*$-algebra and $E$ be a Banach space with
the Radon-Nikodym property. We prove that if $j$ is an embedding
of $E$ into an injective Banach space then for every absolutely
summing operator $T:\mathcal{A}\longrightarrow E$, the composition
$j \circ T$ factors through a diagonal operator from $l^{2}$ into
$l^{1}$. In particular, $T$ factors through a Banach space with
the Schur property. Similarly, we prove that for $2 Keywords:$C^*$-algebras, summing operators, diagonal operators,, Radon-Nikodym property Categories:46L50, 47D15 |
47. CMB 2004 (vol 47 pp. 504)
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High Frequency Resolvent Estimates and Energy Decay of Solutions to the Wave Equation We prove an uniform H\"older continuity of the resolvent of
the Laplace-Beltrami operator on the real axis for a class
of asymptotically Euclidean Riemannian manifolds. As an application we
extend a result of Burq on the behaviour of the
local energy of solutions to the wave equation.
Categories:35B37, 35J15, 47F05 |
48. CMB 2004 (vol 47 pp. 369)
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Spectrally Bounded Linear Maps on ${\cal B}(X)$ We characterize surjective linear maps on ${\cal B}(X)$ that are
spectrally bounded and spectrally bounded below.
Keywords:spectrally bounded linear map. Category:47B49 |
49. CMB 2004 (vol 47 pp. 456)
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On the Berger-Coburn-Lebow Problem for Hardy Submodules In this paper we shall give
an affirmative solution to a problem, posed by Berger, Coburn and Lebow,
for $C^{\ast}$-algebras on Hardy submodules.
Keywords:Hardy submodules Category:47B38 |
50. CMB 2004 (vol 47 pp. 257)
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A Geometric Characterization of Nonnegative Bands A band is a semigroup of idempotent operators. A nonnegative band
$\cls$ in $\clb(\cll^2 (\clx))$ having at least one element of finite
rank and with rank $(S) > 1 $ for all $S$ in $\cls$ is known to have a
special kind of common invariant subspace which is termed
a standard subspace (defined below).
Such bands are called decomposable. Decomposability has helped to
understand the structure of nonnegative bands with constant finite
rank. In this paper, a geometric characterization of maximal,
rank-one, indecomposable nonnegative bands is obtained which
facilitates the understanding of their geometric structure.
Categories:47D03, 47A15 |
