The splitting property for \((p,S)\)-summing operators
type: Item
instance of: scholarly article
title: The splitting property for \((p,S)\)-summing operators
zbMATH Open document ID: 1422.47027
author: Dumitrŭ Popa
published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
publication date: 2017-01-31T00:00:00Z
review text: Let \(X,Y\) be Banach spaces. An absolutely \(\left( p;q\right) \)-summing operator is a continuous linear operator \(T:X\rightarrow Y\) such that \( \left( T(x_{j}\right) )_{j=1}^{\infty }\in \ell_{p}(Y)\) whenever \( \sup_{\varphi \in B_{Y^{\ast }}}\sum\limits_{j=1}^{\infty }\left| \varphi (x_{j})\right| ^{q}<\infty , \) where \(B_{Y^{\ast }}\) denotes the closed unit ball of the dual of \(Y.\) There are several possible extensions of this notion to the multilinear setting: absolutely summing multilinear operators, multiple summing multilinear operators, dominated multilinear operators, strongly summing multilinear operators, strongly multiple summing multilinear operators, etc. In this paper, the author introduces the interesting notion of \((p,S)\)-summing operators. Several properties are proved, such as a domination theorem, a splitting lemma and a composition theorem.
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 47L20
zbMATH DE Number: 6679195
zbMATH Keywords: absolutely summing operators
zbMATH Keywords: operator ideals
zbMATH Keywords: \(p\)-summing operators
zbMATH Keywords: mixing operators
zbMATH Keywords: splitting property
reviewed by: Daniel Pellegrino
MaRDI profile type: Publication
full work available at URL: s13398-016-0284-4
OpenAlex ID: W2267266221
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DOI: 10.1007/S13398-016-0284-4
description: scientific article; zbMATH DE number 6679195