Operators on locally Hilbert space
type: Item
instance of: scholarly article
title: Operators on locally Hilbert space
zbMATH Open document ID: 1364.46050
author: Dinesh J. Karia
author: Yogita M. Parmar
published in: The Journal of Analysis
publication date: 2016-11-10T00:00:00Z
review text: The authors study the pro-\(C^*\)-algebra \(L(H)\) defined on a locally Hilbert space \(H\). Utilizing the Arens-Michael decomposition, they decompose the operators in \(L(H)\) and try to repair a gap found in the Arens-Michael decomposition of \(L(H)\) in [Topological algebras with involution. Amsterdam: Elsevier/North-Holland (2005; Zbl 1197.46001), Remarks (i), pp. 107--108] by \textit{M. Fragoulopoulou}. They also investigate the algebra \(K(H)\) of compact operators. The rank one operators and minimal projections in the setup of locally Hilbert spaces are also studied. They obtain the polar decomposition of an operator in \(L(H)\) by exploiting the inverse limit system. Finally, they introduce the Schatten class operators including the trace class operators and the Hilbert-Schmidt operators.
reviewed by: Mohammad Sal Moslehian
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 46K10
Mathematics Subject Classification ID: 47C15
Mathematics Subject Classification ID: 47B10
zbMATH DE Number: 6651351
zbMATH Keywords: locally Hilbert space
zbMATH Keywords: locally \(m\)-convex \(H^*\)-algebra
zbMATH Keywords: pro-\(C^*\)-algebra
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6651351