Generalized s-numbers of \(\tau\)-measurable operators
type: Item
instance of: scholarly article
title: Generalized s-numbers of \(\tau\)-measurable operators
zbMATH Open document ID: 0617.46063
author: Thierry Fack
author: Hideki Kosaki
published in: Pacific Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Let M be a semi-finite von Neumann algebra and \(\tau\) a faithful trace of M. A densely defined closed oprator T affiliated with M is said to be \(\tau\)-measurable if for each \(\epsilon >0\) there exists a projection E in M such that \(E({\mathcal H})\subseteq\) domain of and \(\tau(I-E)\leq \epsilon\). Let T be \(\tau\)-measurable operator and \(t>0\). The \(t^{th}\) singular number of T is \[ u_ t(T):\inf \{\| TE\|:E\text{ a projection in M, }\tau(I-e)\leq t\}. \] This is an expository article on singular numbers of measurable operators. Applications to dominated convergence theorems and convexity inequalities are investigated.
Mathematics Subject Classification ID: 46L51
Mathematics Subject Classification ID: 46L53
Mathematics Subject Classification ID: 46L54
Mathematics Subject Classification ID: 47B10
zbMATH DE Number: 4000769
zbMATH Keywords: generalized s-numbers of \(\tau\)-measurable operators affiliated with a semi-finite von Neumann algebra
zbMATH Keywords: faithful trace
zbMATH Keywords: singular numbers of measurable operators
zbMATH Keywords: dominated convergence theorems
zbMATH Keywords: convexity inequalities
MaRDI profile type: Publication
full work available at URL: pjm.1986.123.269
OpenAlex ID: W2009307976
DOI: 10.2140/PJM.1986.123.269
description: scientific article; zbMATH DE number 4000769