On the geometry of the set of square roots of elements in \(C^*\)- algebras
type: Item
instance of: scholarly article
title: On the geometry of the set of square roots of elements in \(C^*\)- algebras
zbMATH Open document ID: 0826.46047
DOI: 10.1007/BF01203667
published in: Integral Equations and Operator Theory
publication date: 1995-11-27T00:00:00Z
review text: In the last years, a long series of papers dealing with problems from differential geometry in the context of Banach and \(C^*\)-algebras, has appeared. Thus, Gramsch studied the set of relatively regular operators, Martin studied the space of projective representations of a compact group in a \(C^*\)-algebra, Corach, Porta and Recht studied the set of idempotent elements in a \(C^*\)-algebra, the set of partitions of the identity in a Banach algebra, the set of selfadjoint invertible elements in a \(C^*\)-algebra and the set of positive invertible elements in a \(C^*\)-algebra; Andruchow and Stojanoff considered the differential structure of nilpotent operators on a Hilbert space, the geometry of unitary orbits in \(C^*\)-algebras, and in a joint work with Recht, the geometry of the space of spectral measures with values in a von Neumann algebra. In this paper we study the geometric structure of two spaces related to the set of idempotents and the set of selfadjoint invertible elements in a \(C^*\)-algebra.
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 638262
zbMATH Keywords: infinite-dimensional manifolds
zbMATH Keywords: differential geometry
zbMATH Keywords: Banach and \(C^*\)-algebras
zbMATH Keywords: relatively regular operators
zbMATH Keywords: projective representations of a compact group
zbMATH Keywords: partitions of the identity in a Banach algebra
zbMATH Keywords: selfadjoint invertible elements in a \(C^*\)-algebra
zbMATH Keywords: geometry of unitary orbits in \(C^*\)-algebras
zbMATH Keywords: idempotents
zbMATH Keywords: set of selfadjoint invertible elements in a \(C^*\)-algebra
author: A. Maestripieri
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01203667
OpenAlex ID: W2012870544
description: scientific article; zbMATH DE number 638262