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Hilbert space fusion frames are a natural extension of Hilbert space frames, extending the notion from a set of vectors in a Hilbert space to a set of subspaces of a Hilbert space with analogous notions of overcompleteness and boundedness.…

Functional Analysis · Mathematics 2017-06-23 Mozhgan Mohammadpour , Brian Tuomanen , Rajab Ali Kamyabi Gol

In this notes unbounded regular operators on Hilbert $C^*$-modules over arbitrary $C^*$-algebras are discussed. A densely defined operator $t$ possesses an adjoint operator if the graph of $t$ is an orthogonal summand. Moreover, for a…

Operator Algebras · Mathematics 2025-04-29 Michael Frank , Kamran Sharifi

In this paper we introduce and show some new notions and results on cg-frames of Hilbert spaces. We define cg-orthonormal bases for a Hilbert space H and verify their properties and relations with cg-frames. Actually, we present that every…

Functional Analysis · Mathematics 2019-05-20 Morteza Rahmani

In this manuscript, the concept of dual and approximate dual for continuous frames in Hilbert spaces will be introduced. Some of its properties will be studied. Also, the relations between two continuous Riesz bases in Hilbert spaces will…

Functional Analysis · Mathematics 2017-06-14 Asghar Rahimi , Zahra Darvishi , Bayaz Daraby

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

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

In this article, we define operator algebras internal to a rigid C*-tensor category $\mathcal{C}$. A C*/W*-algebra object in $\mathcal{C}$ is an algebra object $\mathbf{A}$ in $\operatorname{ind}$-$\mathcal{C}$ whose category of free…

Operator Algebras · Mathematics 2017-09-13 Corey Jones , David Penneys

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 study two notions of largeness for closed submodules of Hilbert C*-modules: essentiality and topological essentiality. While the analogous properties are known to be equivalent for closed two-sided ideals of C*-algebras, the one-sided…

Operator Algebras · Mathematics 2026-04-14 Kirill Kartvelishvili

This paper explores the concept of $K$-$g$-frames in locally $C^*$-algebras, which are shown to be more general than $g$-frames. The authors first introduce the notion of a $g$-orthonormal basis and utilize it to define the $g$-operator, a…

Operator Algebras · Mathematics 2024-05-30 Roumaissae Eljazzar , Mohammed Mouniane , Mohamed Rossafi

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 in recent years. This new Theory have been extended from Hilbert spaces to Hilbert C*-modules. In this paper, we introduce the notion of dual *-K-g-frames in Hilbert A-modules. Lastly we study…

Operator Algebras · Mathematics 2021-10-01 M'hamed Ghiati , Samir Kabbaj , Hatim Labrigui , Abdeslam Touri , Mohamed Rossafi

We investigate orthonormality-preserving, C*-conformal and conformal module mappings on Hilbert C*-modules to obtain their general structure. Orthogonality-preserving bounded module maps T act as a multiplication by an element \lambda of…

Operator Algebras · Mathematics 2025-04-29 Michael Frank , Alexander S. Mishchenko , Alexander A. Pavlov

Extending the notion of parallelism we introduce the concept of approximate parallelism in normed spaces and then substantially restrict ourselves to the setting of Hilbert space operators endowed with the operator norm. We present several…

Functional Analysis · Mathematics 2019-08-15 Mohammad Sal Moslehian , Ali Zamani

In the present paper, we investigate some properties of duals of continuous frames in Hilbert C*-modules. In particular, we give requirements so that by removing some elements of a continuous frame, it does not remain a continuous frame and…

Functional Analysis · Mathematics 2023-04-25 Hadi Ghasemi , Tayebe Lal Shateri

A new notion in frame theory, so called weaving frames has been recently introduced to deal with some problems in signal processing and wireless sensor networks. Also, fusion frames are an important extension of frames, used in many areas…

Functional Analysis · Mathematics 2018-02-12 Fahimeh Arabyani Neyshaburi , Ali Akbar Arefijamaal

Frame Theory has a great revolution in recent years. This Theory have been extended from Hilbert spaces to Hilbert $C^{\ast}$-modules. In this paper we consider the stability of continuous operator frame and continuous $K$-operator frames…

Functional Analysis · Mathematics 2021-01-13 A. Touri

In the paper we describe the C*-algebras of noncommutative spherical tight frames over some C*-algebras and then apply to study the noncommutative version of the universal classifying space.

K-Theory and Homology · Mathematics 2007-05-23 Do Ngoc Diep

To a generalized tight continuous frame in a Hilbert space $\H$ indexed by a locally compact space $\Si$ endowed with a Radon measure, one associates a coorbit theory converting spaces of functions on $\Si$ in spaces of vectors comparable…

Functional Analysis · Mathematics 2014-06-30 M. Mantoiu , D. Parra

Hilbert(ian) A-modules over finite von Neumann algebras A with a faithful normal trace state (from global analysis) and Hilbert W*-modules over A (from operator algebra theory) are compared, and a categorical equivalence is established. The…

Operator Algebras · Mathematics 2025-05-08 Michael Frank