On the systems of finite weights on the algebra of bounded operators and corresponding translation invariant measures
type: Item
instance of: scholarly article
title: On the systems of finite weights on the algebra of bounded operators and corresponding translation invariant measures
zbMATH Open document ID: 1433.46042
DOI: 10.1134/S1995080219080067
author: V. Zh. Sakbaev
author: Airat Bikchentaev
published in: Lobachevskii Journal of Mathematics
publication date: 2019-12-03T00:00:00Z
review text: The authors describe the class of translation invariant measures on the algebra \(B(H)\) of bounded linear operators on a Hilbert space \(H\) and some of its subalgebras. Indeed, the authors study the properties of countable additivity, \(\sigma\)-finiteness, local finiteness of the constructed measure \(\lambda\), and the invariance of this measure with respect to some transformations of the algebra \(A\) is considered. Furthermore, they investigate the operator intervals in the Jordan algebra \(B(H)^{sa}\) and obtain some new operator inequalities.
reviewed by: Ghadir Sadeghi
Mathematics Subject Classification ID: 46L51
Mathematics Subject Classification ID: 47L30
Mathematics Subject Classification ID: 47A63
zbMATH DE Number: 7139450
zbMATH Keywords: Hilbert space
zbMATH Keywords: projection
zbMATH Keywords: operator interval
zbMATH Keywords: Jordan algebra
zbMATH Keywords: translation invariant measure
zbMATH Keywords: trace
zbMATH Keywords: Hilbert-Schmidt operator
zbMATH Keywords: operator inequality
zbMATH Keywords: convexity
MaRDI profile type: Publication
cites work: Q5846810
cites work: On sets of measurable operators convex and closed in topology of convergence in measure
cites work: When weak and local measure convergence implies norm convergence
cites work: Averaging of random walks and shift-invariant measures on a Hilbert space
cites work: Q3997462
cites work: Q3534635
cites work: "Lebesgue Measure" on R ∞
cites work: Q4120977
cites work: On Hermitian operators \(X\) and \(Y\) meeting the condition \(-Y\leq X\leq Y\)
cites work: Measures on orthoideals and \(L_1\)-spaces associated with positive operators
cites work: \(L_1\)-space for a positive operator affiliated with von Neumann algebra
cites work: On p-convexity and q-concavity of unitary matrix spaces
cites work: Block projection operators in normed solid spaces of measurable operators
cites work: On a lemma of Berezin
cites work: On the Extreme Points of the Interval Between two Operators
cites work: Q3854185
full work available at URL: s1995080219080067
OpenAlex ID: W2972228051
description: scientific article; zbMATH DE number 7139450