Geometric operator inequalities
type: Item
instance of: scholarly article
title: Geometric operator inequalities
zbMATH Open document ID: 0920.47017
DOI: 10.1016/S0024-3795(96)00201-7
published in: Linear Algebra and its Applications
publication date: 1999-04-18T00:00:00Z
review text: In a given \(C^*\)-algebra there are several interesting subsets (e.g., the set of idempotent elements, the set of selfadjoint invertible elements, the set of nilpotent elements of a given order, the similarity and unitary orbits of elements etc.) that have a differentiable structure and in which the length of curves is measured by means of a Finsler metric. The construction of this metric on the given such set depends on some operator inequalities. The paper contains a fairly complete discussion relating the differential geometry and such operator inequalities. The authors also prove some spectral properties of transformations related to these inequalities.
Mathematics Subject Classification ID: 47A63
Mathematics Subject Classification ID: 47A30
zbMATH DE Number: 1026444
zbMATH Keywords: \(C^*\)-algebra
zbMATH Keywords: idempotent elements
zbMATH Keywords: selfadjoint invertible elements
zbMATH Keywords: nilpotent elements
zbMATH Keywords: similarity and unitary orbits of elements
zbMATH Keywords: length of curves
zbMATH Keywords: Finsler metric
zbMATH Keywords: differential geometry
zbMATH Keywords: operator inequalities
Wikidata QID: Q88554095
author: Esteban Andruchow
author: Gustavo Corach
author: Demetrio Stojanoff
reviewed by: Florian-Horia Vasilescu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1026444