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Related papers: Semi-Fredholm Theory on Hilbert C*-modules

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We provide an equivariant extension of the bivariant Cuntz semigroup introduced in previous work for the case of compact group actions over C*-algebras. Its functoriality properties are explored and some well-known classification results…

Operator Algebras · Mathematics 2016-07-11 Gabriele N. Tornetta

Consider a countably generated Hilbert $C^*$-module $\mathcal M$ over a $C^*$-algebra $\mathcal A$. There is a measure of noncompactness $\lambda$ defined, roughly as the distance from finitely generated projective submodules, which is…

Operator Algebras · Mathematics 2024-09-05 Dragoljub J. Kečkić , Zlatko Lazović

The parallel sum for adjoinable operators on Hilbert $C^*$-modules is introduced and studied. Some results known for matrices and bounded linear operators on Hilbert spaces are generalized to the case of adjointable operators on Hilbert…

Operator Algebras · Mathematics 2018-07-16 Wei Luo , Chuanning Song , Qingxiang Xu

This paper deals mainly with some aspects of the adjointable operators on Hilbert $C^*$-modules. A new tool called the generalized polar decomposition for each adjointable operator is introduced and clarified. As an application, the general…

Functional Analysis · Mathematics 2024-04-25 Xiaofeng Zhang , Xiaoyi Tian , Qingxiang Xu

In this expository note, we present a simple proof of the Fredholm Alternative for compact operators that are norm limits of finite rank operators. We also prove a Fredholm Alternative for pseudodifferential operators of order < 0.

Functional Analysis · Mathematics 2010-11-15 Otgonbayar Uuye

The aim of this article is to extend the results of Asadi M.B, B.V.R. Bhat, G. Ramesh, K. Sumesh about completely positive maps on Hilbert C*-modules. We prove a Stinespring type theorem for a finite family of completely positive maps on…

Operator Algebras · Mathematics 2012-10-23 Marat Pliev

Let $G=K\ltimes A$ be the semi-direct product group of a compact group $K$ acting on an abelian locally compact group $A$. We describe the $C^*$-algebra $C^*(G)$ of $G$ in terms of an algebra of operator fields defined over the spectrum of…

Operator Algebras · Mathematics 2019-04-23 Hedi Regeiba , Jean Ludwig

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

In this paper, we solve a spectral problem about positive semi-definite trace-class pseudodifferential operators on modulation spaces which was posed by H. Feichtinger. Later, C. Heil and D. Larson rephrased the problem in the broader…

Classical Analysis and ODEs · Mathematics 2018-12-11 Radu Balan , Kasso A. Okoudjou , Anirudha Poria

We consider a class of C*-algebras associated to one parameter continuous tensor product systems of Hilbert modules, which can be viewed as continuous counterparts of Pimsner's Toeplitz algebras. By exhibiting a homotopy of…

Operator Algebras · Mathematics 2007-05-23 Ilan Hirshberg

The aim of this paper is to give new characterizations of some fundamental issues about idempotents. In the general setting of adjointable operators on Hilbert $C^*$-modules, a new term of quasi-projection pair is introduced. For each…

Operator Algebras · Mathematics 2025-08-15 Xiaoyi Tian , Qingxiang Xu , Chunhong Fu

In this paper we show that quasisimilar $n$-tuples of tensor products of $m$-isometric operators have the same spectra, essential spectra and indices. The properties of single Fredholm operators possess \cite{4} is related to an important…

Functional Analysis · Mathematics 2025-10-13 Salah Mecheri

In this paper, we introduce notions called inverse set and inverse correspondence over inverse semigroups. These are analogies of Hilbert $C^*$-modules and \Ccorrs in the $C^*$-algebra theory. We show that inverse semigroups and inverse…

Operator Algebras · Mathematics 2024-04-10 Tomoki Uchimura

An operator $T$ on a Hilbert space is called half-centered if the sequence $T^{*}T,(T^{*})^{2}T^{2},...$ consists of mutually commuting operators. It is a subclass of the well-studied centered operators. In this paper we give a condition…

Functional Analysis · Mathematics 2016-02-17 Olof Giselsson

In this paper, we calculate the Frechet derivatives and Mordukhovich derivatives (or coderivatives) of Hilbert Schmidt operators on separable Hilbert spaces, by which we prove that the covering constant for Hilbert-Schmidt operators is…

Functional Analysis · Mathematics 2025-12-04 Jinlu Li

In this paper, we describe the different spectrums of the {\alpha}-times integrated semigroups by the spectrums of their generators. Specially, essential ascent and descent, upper and lower semi-Fredholm and semi-Browder spectrums.

Functional Analysis · Mathematics 2018-01-31 Abdelaziz Tajmouati , Abdeslam El Bakkali , Mohamed Baba Mohamed Ahmed , Hamid Boua

We prove that there exists a pair of "non-isospectral" 1D semiclassical Schr\"odinger operators whose spectra agree modulo h^\infty. In particular, all their semiclassical trace invariants are the same. Our proof is based on an idea of…

Spectral Theory · Mathematics 2015-05-30 Victor Guillemin , Hamid Hezari

Considering the deeper reasons of the appearance of a remarkable counterexample by J.~Kaad and M.~Skeide [17] we consider situations in which two Hilbert C*-modules $M \subset N$ with $M^\bot = \{ 0 \}$ over a fixed C*-algebra $A$ of…

Operator Algebras · Mathematics 2026-04-07 Michael Frank

We generalize some facts about function algebras to operator algebras, using the `noncommutative Shilov boundary' or $C^*$-envelope first considered by Arveson. In the first part we study and characterize complete isometries between…

Operator Algebras · Mathematics 2007-05-23 David P. Blecher , Louis E. Labuschagne

We replace a ring with a small $\mathbb C$-linear category $\mathcal{C}$, seen as a ring with several objects in the sense of Mitchell. We introduce Fredholm modules over this category and construct a Chern character taking values in the…

Category Theory · Mathematics 2021-05-26 Mamta Balodi , Abhishek Banerjee