Manuilov algebra, \(C^\ast\)-Hilbert modules, and Kuiper type theorems
type: Item
instance of: scholarly article
title: Manuilov algebra, \(C^\ast\)-Hilbert modules, and Kuiper type theorems
zbMATH Open document ID: 1415.46038
DOI: 10.1134/S1061920818040118
published in: Russian Journal of Mathematical Physics
publication date: 2019-01-30T00:00:00Z
review text: The author generalizes the $C^*$-algebra generated by matrices of bounded operators in a separable Hilbert space $H$ with a uniformly bounded number of nonzero elements in each row and each column with respect to a fixed basis, introduced recently by the reviewer [``On the $C^*$-algebra of matrix-finite bounded operators'', Preprint, \url{arXiv:1807.11020}], to the case of Hilbert $C^*$-modules. The main result of the paper is contractibility of the groups of invertible elements in these generalized $C^*$- or Banach algebras (Kuiper-type theorems).
reviewed by: Vladimir M. Manuilov
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 46L08
zbMATH DE Number: 7008568
zbMATH Keywords: Kuiper theorem
zbMATH Keywords: Hilbert $C^*$-module
zbMATH Keywords: contractibility of the group of invertible elements
author: E. V. Troitskij
MaRDI profile type: Publication
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full work available at URL: s1061920818040118
OpenAlex ID: W2905180193
description: scientific article; zbMATH DE number 7008568