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Related papers: Continuous biframes in Hilbert $C^{\ast}-$modules

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In this paper, we investigate the invertibility of generalized g-Bessel multipliers. We show that for semi-normalized symbols, the inverse of any invertible generalized g-frame multiplier can be represented as a generalized g-frame…

Functional Analysis · Mathematics 2019-06-18 M. Abolghasemi , Y. Tolooei , Z. Moosavianfard

Let $A$ be a (non-unital, in general) C*-algebra with center $Z(M(A))$ of its multiplier algebra, and let $\{ X, \langle .,. \rangle \}$ be a full Hilbert $A$-module. Then any bijective bounded module morphism $T$, for which every…

Operator Algebras · Mathematics 2026-04-09 Michael Frank

We present a general approach to a modular frame theory in C*-algebras and Hilbert C*-modules. The investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital C*-algebras that possess orthonormal Hilbert…

Operator Algebras · Mathematics 2025-05-08 Michael Frank , David R. Larson

k-frames were recently introduced by Gavruta in Hilbert spaces to study atomic systems with respect to a bounded linear operator. A continuous frame is a family of vectors in Hilbert space which allows reproductions of arbitrary elements by…

Functional Analysis · Mathematics 2019-01-15 Gholamreza Rahimlou , Reza Ahmadi , Mohammad Ali Jafarizadeh , Susan Nami

In this paper, we introduce the concept of continuous $g-$atomic subspace for a bounded linear operator and gives several useful continuous resolution of the identity operator on a Hilbert space by implies the theory of continuous…

Functional Analysis · Mathematics 2024-09-10 Mohamed Rossafi , Fakhr-dine Nhari , Abdeslam Touri

This paper is a detailed study of finite-dimensional modules defined on bicomplex numbers. A number of results are proved on bicomplex square matrices, linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces, including…

Functional Analysis · Mathematics 2011-08-10 Raphael Gervais Lavoie , Louis Marchildon , Dominic Rochon

This paper begins the study of infinite-dimensional modules defined on bicomplex numbers. It generalizes a number of results obtained with finite-dimensional bicomplex modules. The central concept introduced is the one of a bicomplex…

Functional Analysis · Mathematics 2011-08-10 Raphael Gervais Lavoie , Louis Marchildon , Dominic Rochon

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

Frame Theory has a great revolution for recent years. This theory has been extended from Hilbert spaces to Hilbert $C^{\ast}$-modules. In this paper, we introduce the concept of Controlled K-operator frame for the space…

Functional Analysis · Mathematics 2020-08-14 Abdeslam Touri , Samir Kabbaj

We construct Hilbert $C^*$-modules useful for studying Gabor systems and show that they are Banach algebras under pointwise multiplication. For rational $ab<1$ we prove that the set of functions $g \in L^2(R)$ so that $(g,a,b)$ is a Bessel…

Functional Analysis · Mathematics 2007-05-23 Michael Coco , M. C. Lammers

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

In this note, we first introduce the notation of weaving cfusion frames in separable Hilbert spaces. After reviewing the conditions for maintaining the weaving c-fusion frames under the bounded linear operator and also, removing vectors…

Functional Analysis · Mathematics 2019-01-15 Vahid Sadri , Reza Ahmadi , Gholamreza Rahimlou

Frame theory is recently an active research area in mathematics, computer science and engineering with many exciting applications in a variety of different fields. This theory has been generalized rapidly and various generalizations of…

Functional Analysis · Mathematics 2020-11-25 Mohamed Rossafi , Brahim Moalige , Hamid Faraj , Abdeslam Touri , Samir Kabbaj

Frame Theory has a great revolution for recent years. This theory has been extended from Hilbert spaces to Hilbert $C^{\ast}$-modules. In this paper, we introduce the concept of Controlled $\ast$-$K$-operator frame for the space…

Functional Analysis · Mathematics 2023-02-16 Hatim Labrigui , Mohamed Rossafi , Abdeslam Touri , Nadia Assila

We consider C*-algebras generated by a single Hilbert bimodule (Pimsner-Toeplitz algebras) and by a product systems of Hilbert bimodules. We give a new proof of a theorem of Pimsner, which states that any representation of the generating…

Operator Algebras · Mathematics 2007-05-23 Ilan Hirshberg

The concepts of controlled frames and it's dual in n-Hilbert spaces and their tensor products have been introduced and then some of their characterizations are given. We further study the relationship between controlled frame and bounded…

Functional Analysis · Mathematics 2021-09-06 Prasenjit Ghosh , T. K. Samanta

We study fusion frame in tensor product of Hilbert spaces and discuss some of its properties. The resolution of the identity operator on a tensor product of Hilbert spaces is being discussed. An alternative dual of a fusion frame in tensor…

Functional Analysis · Mathematics 2024-03-12 Prasenjit Ghosh , T. K. Samanta

In this paper, we will introduce the new concept of K-bi-g-frames for Hilbert spaces. Then, we examine some characterizations with the help of a biframe operator. Finally, we investigate several results about the stability of K-bi-g-frames…

Functional Analysis · Mathematics 2024-03-12 Abdelilah Karara , Mohamed Rossafi

In this paper, we introduce a new concept of K-biframes for Hilbert spaces. We then examine several characterizations with the assistance of a biframe operator. Moreover, we investigate their properties from the perspective of operator…

Functional Analysis · Mathematics 2024-02-15 Abdelilah Karara , Mohamed Rossafi

We introduce and study some new uniform structures for Hilbert $C^*$-modules over an algebra $A$. In particular, we prove that in some cases they have the same totally bounded sets. To define one of them, we introduce a new class of…

Operator Algebras · Mathematics 2024-02-29 Denis Fufaev , Evgenij Troitsky