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Related papers: Sum of $g-$frames in Hilbert $C^{\ast}-$modules

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In this paper, we give some sufficient conditions under which perturbations preserve Hilbert frames and near-Riesz bases. Similar results are also extended to frame sequences, Riesz sequences and Schauder frames. It is worth mentioning that…

Functional Analysis · Mathematics 2013-12-13 Dongyang Chen , Lei Li , Bentuo Zheng

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

The stability theorem for persistent homology is a central result in topological data analysis. While the original formulation of the result concerns the persistence barcodes of $\mathbb{R}$-valued functions, the result was later cast in a…

Algebraic Topology · Mathematics 2018-10-24 Magnus Bakke Botnan , Michael Lesnick

A $*$-bimodule for a unital $*$-algebra $A$ is an $A$-bimodule $X$ which is a vector space with involution $x\mapsto x^+$ satisfying $(a\cdot x\cdot b)^+=b^+\cdot x^+\cdot b^+$ for $x\in X$ and $a,b\in A$. An algebraic model for…

Operator Algebras · Mathematics 2020-08-14 Konrad Schmüdgen

Let $A$ be a normal operator in a Hilbert space $\mathcal{H}$, and let $\mathcal{G} \subset \mathcal{H}$ be a countable set of vectors. We investigate the relations between $A$, $\mathcal{G}$ , and $L$ that makes the system of iterations…

Functional Analysis · Mathematics 2016-11-02 A. Aldroubi , C. Cabrelli , A. F. Çakmak , U. Molter , A. Petrosyan

In this paper, we will introduce a new notion, that of $K$-Integral operator frames in the set of all bounded linear operators noted $\mathcal{B}(H)$, where $H$ is a separable Hilbert space. Also, we prove some results of integral…

Functional Analysis · Mathematics 2020-08-13 Hatim Labrigui , Mohamed Rossafi , Abdeslam Touri , Samir Kabbaj

We study representations of Hilbert bimodules on pairs of Hilbert spaces. If $A$ is a C*-algebra and $\mathsf{X}$ is a right Hilbert $A$-module, we use such representations to faithfully represent the C*-algebras $\mathcal{K}_A(\mathsf{X})$…

Operator Algebras · Mathematics 2024-10-18 Alonso Delfín

In this paper we discuss some topics related to the general theory of frames. In particular we focus our attention to the existence of different 'reconstruction formulas' for a given vector of a certain Hilbert space and to some refinement…

funct-an · Mathematics 2008-02-03 Fabio Bagarello

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

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

In this paper, we provide some generalization of the concept of fusion frames following that evaluate their representability via a linear operator in Hilbert $C*$-module. We assume that $\Upsilon _\xi$ is self-adjoint and $\Upsilon…

Functional Analysis · Mathematics 2023-12-06 Abdelilah Karara , Roumaissae Eljazzar , Hassan Sfouli

This is a graduate-level introduction to C*-algebras, Hilbert C*-modules, vector bundles, and induced representations of groups and C*-algebras, with applications to quantization theory, phase space localization, and configuration space…

Mathematical Physics · Physics 2007-05-23 N. P. Landsman

Let F be a right Hilbert C*-module over a C*-algebra B, and suppose that F is equipped with a left action, by compact operators, of a second C*-algebra A. Tensor product with F gives a functor from Hilbert C*-modules over A to Hilbert…

Operator Algebras · Mathematics 2020-06-19 Tyrone Crisp

In this paper, we introduce and we study the concept of Continuous Controlled K-Frame for Hilbert $C^{\ast}$-Modules wich are generalizations of discrete Controlled K-Frames.

Functional Analysis · Mathematics 2021-10-06 Hamid Faraj , Samir Kabbaj , Hatim Labrigui , Abdeslam Touri , Mohamed Rossafi

Frames play an important role in various practical problems related to signal and image processing. In this paper, we define computable frames in computable Hilbert spaces and obtain computable versions of some of their characterizations.…

Functional Analysis · Mathematics 2018-01-12 Poonam Mantry , S. K. Kaushik

A classical result of Duffin and Schaeffer gives conditions under which a discrete collection of characters on $\mathbb{R}$, restricted to $E = (-1/2, 1/2)$, forms a Hilbert-space frame for $L^2(E)$. For the case of characters with period…

Representation Theory · Mathematics 2014-09-30 Benjamin Robinson , William Moran , Douglas Cochran , Stephen D. Howard

Given a frame in a finite dimensional Hilbert space we construct additive perturbations which decrease the condition number of the frame. By iterating this perturbation, we introduce an algorithm that produces a tight frame in a finite…

Functional Analysis · Mathematics 2025-06-19 Oleg Asipchuk , Jacob Glidewell , Luis Rodriguez

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

In this paper we survey our recent work on C*-correspondences and their associated operator algebras; in particular, on adding tails, the Shift Equivalence Problem and Hilbert bimodules.

Operator Algebras · Mathematics 2014-04-08 Evgenios T. A. Kakariadis , Elias G. Katsoulis

Continuous frames and tensor products are important topics in theoretical physics. This paper combines those concepts. We derive fundamental properties of continuous frames for tensor product of Hilbert spaces. This includes, for example,…

Functional Analysis · Mathematics 2022-03-23 Peter Balazs , Nenad Teofanov