Canonical operator space structures on non-commutative \(L^p\) spaces
type: Item
instance of: scholarly article
title: Canonical operator space structures on non-commutative \(L^p\) spaces
zbMATH Open document ID: 0955.46029
author: Francesco Fidaleo
published in: Journal of Functional Analysis
publication date: 2001-02-21T00:00:00Z
review text: The author studies canonical operator space structures on the non-commutative spaces \(L^p_\eta(M,\phi,\omega)\) constructed by a Stein-Weiss interpolation procedure. Here, \(\phi\), \(\psi\) are two semifinite faithful weights on a \(W^*\)-algebra \(M\). It is shown that all such spaces for \(0\leq \eta\leq 1\) and arbitrary \(\phi\), \(\psi\) are completely isomorphic as operator spaces, i.e. \(L^p_{\eta_1}(M, \phi_1,\omega_1)\cong L^p_{\eta_2}(M, \phi_2,\omega_2)\). The paper also contains a description of the norms on all matrix spaces of the operator space \(L^p(M)\).
Mathematics Subject Classification ID: 46L07
Mathematics Subject Classification ID: 46L52
Mathematics Subject Classification ID: 47L25
zbMATH DE Number: 1398380
zbMATH Keywords: canonical operator space structures
zbMATH Keywords: non-commutative spaces
zbMATH Keywords: Stein-Weiss interpolation procedure
zbMATH Keywords: semifinite faithful weights
zbMATH Keywords: \(W^*\)-algebra
zbMATH Keywords: matrix spaces
reviewed by: Khristo N. Boyadzhiev
MaRDI profile type: Publication
full work available at URL: jfan.1999.3498
OpenAlex ID: W2081127853
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DOI: 10.1006/JFAN.1999.3498
description: scientific article; zbMATH DE number 1398380