Complemented subspaces isomorphic to \(\ell_ p\) in tensor products and operator spaces
type: Item
instance of: scholarly article
title: Complemented subspaces isomorphic to \(\ell_ p\) in tensor products and operator spaces
zbMATH Open document ID: 0783.46017
published in: Siberian Mathematical Journal
publication date: 1993-03-28T00:00:00Z
review text: The principal results obtained in the paper are the following: 1. Suppose that \(1\leq q<p\leq r\leq \infty\). If a Banach space \(X\) has no complemented subspaces isomorphic to \(\ell_ q\), then \(X\otimes_{\varepsilon_ r}\ell_ p\) does not contain complemented subspaces isomorphic to \(\ell_ q\). 2. Suppose that \(1\leq r\leq p<q\leq\infty\). If a Banach space \(X\) has no complemented subspaces isomorphic to \(\ell_ q\), then \(\ell_ p\otimes_{g_ r}X\) does not contain complemented subspaces isomorphic to \(\ell_ q\).
Mathematics Subject Classification ID: 46B25
Mathematics Subject Classification ID: 46B28
zbMATH DE Number: 130859
zbMATH Keywords: tensor products
zbMATH Keywords: spaces of operators
zbMATH Keywords: complemented subspaces
author: Eve Oja
reviewed by: S. S. Kutateladze
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 130859