Operators defined on projective and natural tensor products
type: Item
instance of: scholarly article
title: Operators defined on projective and natural tensor products
zbMATH Open document ID: 0808.47020
published in: Michigan Mathematical Journal
publication date: 1995-03-15T00:00:00Z
review text: This paper studies the behaviour of operators defined on the projective and natural tensor product of an \(\ell_ p\) space and an arbitrary Banach space \(X\). The main result is the following: If \(E\) and \(F\) are Banach spaces, \(E\) not containing \(\ell_ 1\), and all operators from \(E\) into \(\ell_ p\) and all operators from \(E\) into \(F\) are compact, then all operators from \(E\) into \(\ell_ p\widehat\otimes_ \pi X\) are compact. Two applications of the techniques involved in the proof of this result are considered: a study of the tensor stability (with respect to the projective and natural tensor product with an \(\ell_ p\)-space) of the scale of operator ideals formed by the \(p\)-converging operators for \(1\leq p\leq +\infty\), and a vector-valued version of Pitt's theorem.
Mathematics Subject Classification ID: 47A80
Mathematics Subject Classification ID: 46M05
Mathematics Subject Classification ID: 47B07
Mathematics Subject Classification ID: 47L20
zbMATH DE Number: 474979
zbMATH Keywords: operators defined on projective and natural tensor products
zbMATH Keywords: compact operator
zbMATH Keywords: tensor stability
zbMATH Keywords: scale of operator ideals formed by the \(p\)- converging operators
zbMATH Keywords: vector-valued version of Pitt's theorem
author: Jesús M. F. Castillo
author: J. A. López Molina
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029004761
OpenAlex ID: W1963493226
DOI: 10.1307/MMJ/1029004761
description: scientific article; zbMATH DE number 474979