Automatic continuity of orthogonality preservers on a non-commutative \(L^p(\tau)\) space
type: Item
instance of: scholarly article
title: Automatic continuity of orthogonality preservers on a non-commutative \(L^p(\tau)\) space
zbMATH Open document ID: 1288.47034
author: Antonio M. Peralta
author: T. Oikhberg
published in: Journal of Functional Analysis
publication date: 2013-04-30T00:00:00Z
review text: Suppose that \(M\) is a von Neumann algebra on a Hilbert space \(H\) equipped with a normal semifinite faithful trace \(\tau\). Denote by \(\mathfrak{C}\) the set of all linear combinations of positive elements \(a\in M\) with \(\tau(\text{supp}(a))<\infty\). The space \(L^p(M,\tau)\) is the completion of \(\mathfrak{C}\) in the norm \(\|\cdot\|_p\). Suppose that \(T\) is an orthogonality-to-\(p\)-orthogonality preserving linear map from \(L^p(M,\tau)\) into a Banach space \(X\). In the paper under review, the authors discuss the automatic continuity of \(T\) for some von Neumannn algebras \(M\).
Mathematics Subject Classification ID: 47B49
Mathematics Subject Classification ID: 46L52
zbMATH DE Number: 6159669
zbMATH Keywords: non-commutative \(L^p\) spaces
zbMATH Keywords: orthogonality preserving operators
reviewed by: Qi Xiaofei
MaRDI profile type: Publication
full work available at URL: j.jfa.2013.01.019
OpenAlex ID: W2007147823
DOI: 10.1016/J.JFA.2013.01.019
description: scientific article; zbMATH DE number 6159669