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Related papers: Exact Continuous frames in Hilbert C*-modules

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We investigate complexes of Hilbert C*-modules, which are cochain complexes with (unbounded) regular operators between Hilbert C*-modules as differential maps. In particular, we provide various equivalent characterizations of the Fredholm…

Operator Algebras · Mathematics 2025-05-13 Brian Villegas-Villalpando , Koen van den Dungen

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

The main purpose is to introduce the so-called bicomplex (bc)-frames which is a special extension to bicomplex infinite Hilbert spaces of the classical frames. The crucial result is the characterization of bc-frames in terms of their…

Functional Analysis · Mathematics 2020-01-22 Aiad El Gourari , Allal Ghanmi , Mohammed Souid El Ainin

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

We introduce the notion of Hilbert $C^*$-module independence: Let $\mathscr{A}$ be a unital $C^*$-algebra and let $\mathscr{E}_i\subseteq \mathscr{E},\,\,i=1, 2$, be ternary subspaces of a Hilbert $\mathscr{A}$-module $\mathscr{E}$. Then…

Operator Algebras · Mathematics 2021-04-20 R. Eskandari , J. Hamhalter , M. S. Moslehian , V. M. Manuilov

A $C^*$-textile dynamical system $({\cal A}, \rho,\eta,\Sigma^\rho,\Sigma^\eta, \kappa)$ connsists of a unital $C^*$-algebra ${\cal A}$, two families of endomorphisms ${\rho_\alpha}_{\alpha \in \Sigma^\rho}$ and ${\eta_a}_{a \in…

Operator Algebras · Mathematics 2011-11-15 Kengo Matsumoto

A C*-algebra $A$ is C*-reflexive if any countably generated Hilbert C*-module $M$ over $A$ is C*-reflexive, i.e. the second dual module $M''$ coincides with $M$. We show that a commutative C*-algebra $A$ is C*-reflexive if and only if for…

Operator Algebras · Mathematics 2010-01-08 M. Frank , V. Manuilov , E. Troitsky

A $\Sigma^*$-algebra is a concrete $C^*$-algebra that is sequentially closed in the weak operator topology. We study an appropriate class of $C^*$-modules over $\Sigma^*$-algebras analogous to the class of $W^*$-modules (selfdual…

Operator Algebras · Mathematics 2016-09-13 Clifford A. Bearden

Generalizing a definition by Kalra \cite{Kalra}, the purpose of this paper is to analyze cyclic frames in finite-dimensional Hilbert spaces. Cyclic frames form a subclass of the dynamical frames introduced and analyzed in detail by Aldroubi…

Functional Analysis · Mathematics 2025-08-26 Ole Christensen , Navneet Redhu , Niraj K. Shukla

Fusion frames are a very active area of research today because of their myriad of applications in pure mathematics, applied mathematics, engineering, medicine, signal and image processing and much more. They provide a great flexibility for…

In this paper we study structural properties of the Cuntz semigroup and its functionals for continuous fields of C*-algebras over finite dimensional spaces. In a variety of cases, this leads to an answer to a conjecture posed by Blackadar…

Operator Algebras · Mathematics 2013-06-07 Ramon Antoine , Joan Bosa , Francesc Perera , Henning Petzka

Hilbert bimodules are morphisms between C*-algebraic models of quantum systems, while symplectic dual pairs are morphisms between Poisson geometric models of classical systems. Both of these morphisms preserve representation-theoretic…

Mathematical Physics · Physics 2024-05-01 Benjamin H. Feintzeig , Jer Steeger

In this paper, we introduce the concept of semi-continuous $g$-frames in Hilbert spaces. We first construct an example of semi-continuous $g$-frames using the Fourier transform of the Heisenberg group and study the structure of such frames.…

Functional Analysis · Mathematics 2020-11-06 Anirudha Poria

We extend in this paper several results of E. Kirchberg, S. Wassermann and the author dealing with continuous fields of C*--algebras to the semi-continuous case. We provide a new characterisation of separable lower semi-continuity…

Operator Algebras · Mathematics 2016-09-07 Etienne Blanchard

The Kaczmarz algorithm in Hilbert spaces is a classical iterative method for stably recovering vectors from inner product data. In this paper, we extend the algorithm to the setting of Hilbert $C^*$-modules and establish analogues of its…

Functional Analysis · Mathematics 2025-08-20 Daniel Alpay , Chad Berner , Eric S. Weber

In this paper we intend to introduce the concept of c-K-g-frames, which are the generalization of K-g-frames. In addition, we prove some new results on c-K-g-frames on Hilbert spaces. Moreover, we define the related oprators of c-K-g…

Functional Analysis · Mathematics 2019-05-15 E. Alizadeh , M. H. Faroughi , M. Rahmani

We study closedness of the range, adjointability and generalized invertibility of modular operators between Hilbert modules over locally C*-algebras of coefficients. Our investigations and the recent results of M. Frank [Characterizing…

Operator Algebras · Mathematics 2011-08-31 Kamran Sharifi

Fusion frames, and, more generally, operator-valued frame sequences are generalizations of classical frames, which are today a standard notion when redundant, yet stable sequences are required. However, the question of stability of duals…

Functional Analysis · Mathematics 2016-09-01 Gitta Kutyniok , Victoria Paternostro , Friedrich Philipp

In representations using frames, oblique duality appears in situations where the analysis and the synthesis has to be done in different subspaces. In some cases, we cannot obtain an explicit expression for the oblique duals and in others…

Functional Analysis · Mathematics 2023-05-01 Jorge P. Díaz , Sigrid B. Heineken , Patricia M. Morillas

A mapping $f: {\mathcal M} \to {\mathcal N}$ between Hilbert $C^*$-modules approximately preserves the inner product if \[\|< f(x), f(y)> - < x, y> \| \leq \phi(x, y),\] for an appropriate control function $\phi(x,y)$ and all $x, y \in…

Operator Algebras · Mathematics 2008-04-30 Jacek Chmielinski , Mohammad Sal Moslehian