The isometries of \({\mathcal L}(L^P, L^R)\)
type: Item
instance of: scholarly article
title: The isometries of \({\mathcal L}(L^P, L^R)\)
zbMATH Open document ID: 0944.47042
author: Ryszard Grząślewicz
published in: Functiones et Approximatio. Commentarii Mathematici
publication date: 2000-09-14T00:00:00Z
review text: the surjective isometries of the operator space \({\mathcal L}(\ell^p,\ell^{r})\) for \(1<p,r<\infty\) are described: If \(1/p+1/r\neq 1\), then a surjective isometry of this space has the form \(\Phi(T)= VTU\) with \(V\) a surjective isometry of \(\ell^r\) and \(U\) a surjective isometry of \(\ell^p\); if \(1/p+1/r=1\), such a mapping has either the above form or \(\Phi(T)= VT^*U\). Reviewer's remark: In the title of the original article, the spelling \({\mathcal L}(L^P,L^R)\) is wrong and misleading.
reviewed by: Dirk Werner
Mathematics Subject Classification ID: 47L05
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 47B38
zbMATH DE Number: 1251493
zbMATH Keywords: surjective isometries of operator spaces
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1251493