Absolutely \((r,q)\)-summing operators on vector-valued function spaces
type: Item
instance of: scholarly article
title: Absolutely \((r,q)\)-summing operators on vector-valued function spaces
zbMATH Open document ID: 1441.47023
author: Fernando Muñoz
author: Cándido Piñeiro
author: Eve Oja
published in: Integral Equations and Operator Theory
publication date: 2017-12-07T00:00:00Z
review text: For Banach spaces $X,Y,Z$ and a tensor norm $\alpha$, every operator $U\in \mathcal{L}(Z\widehat{\otimes}_{\alpha}X,Y)$ induces an associated operator $U^{\#}\in \mathcal{L}(Z,\mathcal{L}(X,Y))$ by $(U^{\#}z)x=U(z\otimes x)$, $x\in X$ and $z\in Z$. \par The present paper studies the interplay between $U$ and $U^{\#}$ in the context of absolutely $(r,q)$-summing operators by considering the spaces $C_{p}(\Omega ,X)$ of $p$-continuous ($1\leq p\leq \infty$) functions $f$ on a compact Hausdorff space $\Omega$. The authors use tensor product theory to prove the majority of the results.
reviewed by: Elhadj Dahia
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 46E40
Mathematics Subject Classification ID: 46B28
Mathematics Subject Classification ID: 47L20
Mathematics Subject Classification ID: 46G10
Mathematics Subject Classification ID: 46M05
zbMATH DE Number: 6816335
zbMATH Keywords: absolutely $(r,q)$-summing operators
zbMATH Keywords: $p$-continuous vector-valued functions
zbMATH Keywords: Schwartz theorem
MaRDI profile type: Publication
full work available at URL: s00020-017-2376-8
OpenAlex ID: W2615393017
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DOI: 10.1007/S00020-017-2376-8
description: scientific article; zbMATH DE number 6816335