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Related papers: Frames and outer frames for Hilbert C^*-modules

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This paper studies the problems of embedding and isomorphism for countably generated Hilbert C*-modules over commutative C*-algebras. When the fibre dimensions differ sufficiently, relative to the dimension of the spectrum, we show that…

Operator Algebras · Mathematics 2015-06-01 Leonel Robert , Aaron Tikuisis

In this papers we investigate the g-frame and Bessel g-sequence related to a linear bounded operator $K$ in Hilbert $C^{\ast}$-module and we establish some results.

Operator Algebras · Mathematics 2019-01-15 H. Labrigui , A. Touri , S. Kabbaj

In this article, we study tensor product of Hilbert $C^*$-modules and Hilbert spaces. We show that if $E$ is a Hilbert $A$-module and $F$ is a Hilbert $B$-module, then tensor product of frames (orthonormal bases) for $E$ and $F$ produce…

Operator Algebras · Mathematics 2007-05-23 Amir Khosravi , Behrooz Khosravi

It is shown that every linear surjective isometry between two right, full, Hilbert C*-modules is a sum of two maps : a (bi-) module map (which is completely isometric and preserves the inner product) and a map that reverses the (bi-) module…

Operator Algebras · Mathematics 2007-05-23 Baruch Solel

We show that every infinite-dimensional commutative unital C*-algebra has a Hilbert C*-module admitting no frames. In particular, this shows that Kasparov's stabilization theorem for countably generated Hilbert C*-modules can not be…

Operator Algebras · Mathematics 2014-02-26 Hanfeng Li

In this peaper we stady certain Bessel sequences $\left\{f_k\right\}_{k=1}^{\infty}$ in Hilbert C*- modules $\mathcal{H}$ for which operator $S$ defined by \ref{eq2} is of the form $\mathcal{T}+\xi I$, for some real number $\xi$ and a…

Functional Analysis · Mathematics 2024-01-01 Abdelilah Karara , Khadija Mabrouk

Theory of extensions of Hilbert C*-modules was developed by D. Bakic and B. Guljas. An easy observation shows that in the case, when the underlying C*-algebra extension is commutative and the Hilbert C*-modules are projective of finite…

Operator Algebras · Mathematics 2012-03-20 Vladimir Manuilov , Jingming Zhu

It is shown that the metric on the union of the sets $X$ and $Y$ defines a Hilbert $C^*$-module over the uniform Roe algebra of the space $X$ with a fixed metric $d_X$. A number of examples of such Hilbert $C^*$-modules are described.

Operator Algebras · Mathematics 2021-05-11 V. Manuilov

We continue our study of the general theory of possibly nonselfadjoint algebras of operators on a Hilbert space, and modules over such algebras, developing a little more technology to connect `nonselfadjoint operator algebra' with the…

Operator Algebras · Mathematics 2007-05-23 David P. Blecher

The aim of the present paper is to describe self-duality and C*- reflexivity of Hilbert {\bf A}-modules $\cal M$ over monotone complete C*-algebras {\bf A} by the completeness of the unit ball of $\cal M$ with respect to two types of…

funct-an · Mathematics 2025-04-29 Michael Frank

In the first part of the paper we describe the dual \ell^2(A)^{\prime} of the standard Hilbert C*-module \ell^2(A) over an arbitrary (not necessarily unital) C*-algebra A. When A is a von Neumann algebra, this enables us to construct…

Operator Algebras · Mathematics 2019-12-19 Damir Bakic

In the present paper the notion of a Hilbert module over a locally C*-algebra is discussed and some results are obtained on this matter. In particular, we give a detailed proof of the known result that the set of adjointable endomorphisms…

Operator Algebras · Mathematics 2007-05-23 Yu. I. Zhuraev , F. Sharipov

We show that, when $A$ is a separable C*-algebra, every countably generated Hilbert $A$-module is projective (with bounded module maps as morphisms). We also study the approximate extensions of bounded module maps. In the case that $A$ is a…

Operator Algebras · Mathematics 2023-01-12 Lawrence G. Brown , Huaxin Lin

Frames on Hilbert C*-modules have been defined for unital C*-algebras by Frank and Larson and operator valued frames on a Hilbert space have been studied in arXiv.0707.3272v1.[math.FA]. Goal of the present paper is to introduce operator…

Operator Algebras · Mathematics 2007-09-26 Victor Kaftal , David Larson , Shuang Zhang

The duality principle for Gabor frames is one of the pillars of Gabor analysis. We establish a far-reaching generalization to Morita equivalent $C^*$-algebras where the equivalence bimodule is a finitely generated projective Hilbert…

Operator Algebras · Mathematics 2019-05-07 Are Austad , Mads S. Jakobsen , Franz Luef

We single out the concept of concrete Hilbert module over a locally $C^*$-algebra by means of locally bounded operators on certain strictly inductive limits of Hilbert spaces. Using this concept, we construct an operator model for all…

Operator Algebras · Mathematics 2025-11-04 Aurelian Gheondea

The aim of this paper is to present a unified framework in the setting of Hilbert $C^*$-modules for the scalar- and vector-valued reproducing kernel Hilbert spaces and $C^*$-valued reproducing kernel spaces. We investigate conditionally…

Operator Algebras · Mathematics 2021-05-17 M. S. Moslehian

In this article, we study g-frames in Hilbert $C^*$-modules and investigate conditions under which the sum of two g-frames (or a g-frame and a g-Bessel sequence) remains a g-frame. We also address the stability of g-frames under certain…

Functional Analysis · Mathematics 2025-02-19 Abdellatif Lfounoune , Hafida Massit , Abdelilah Karara , Mohamed Rossafi

We study the theory of a Hilbert space H as a module for a unital C*-algebra A from the point of view of continuous logic. We give an explicit axiomatization for this theory and describe the structure of all the representations which are…

Logic · Mathematics 2012-12-03 Camilo Argoty

Improving and extending the concept of dual for frames, fusion frames and continuous frames, the notion of dual for continuous fusion frames in Hilbert spaces will be studied. It will be shown that generally the dual of c-fusion frames may…

Functional Analysis · Mathematics 2016-08-09 Asghar Rahimi , Zahra Darvishi , Bayaz Daraby