On the structure of tensor norms related to \((p,\sigma)\)-absolutely continuous operators
type: Item
instance of: scholarly article
title: On the structure of tensor norms related to \((p,\sigma)\)-absolutely continuous operators
zbMATH Open document ID: 0852.46022
author: E. A. Sánchez-Pérez
published in: Collectanea Mathematica
publication date: 1996-12-09T00:00:00Z
full work available at URL: https://eudml.org/doc/40195
review text: An interpolation norm on tensor products of \(p\)-integrable function spaces and Banach spaces which satisfies intermediate properties between the Bochner norm and the injective norm is defined. Substitutes of the classical Chevet-Persson-Saphar inequalities are obtained for this case. The so-called calculus of traced tensor norms (developed by A. Defant and K. Floret) is used in order to obtain a tensor product description of the tensor norm associated to the interpolated ideal of \((p, \sigma)\)-absolutely continuous operators defined by Jarchow and Matter. This operator ideal is contained in the operator ideal of absolutely continuous operators defined by Niculescu, and is closely related to the ideal of \(p\)-summing operators. As an application we find the largest tensor norm less than or equal to our interpolation norm.
reviewed by: E. A. Sánchez-Pérez
Mathematics Subject Classification ID: 46B28
Mathematics Subject Classification ID: 47L20
Mathematics Subject Classification ID: 46M05
zbMATH DE Number: 894168
zbMATH Keywords: absolutely summing operators
zbMATH Keywords: interpolation norm
zbMATH Keywords: tensor products of \(p\)-integrable function spaces
zbMATH Keywords: Bochner norm
zbMATH Keywords: injective norm
zbMATH Keywords: Chevet-Persson-Saphar inequalities
zbMATH Keywords: interpolated ideal of \((p, \sigma)\)-absolutely continuous operators
zbMATH Keywords: ideal of \(p\)-summing operators
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 894168