Swartz type results for nuclear and multiple 1-summing bilinear operators on \(c_0(\mathcal {X})\times c_0(\mathcal {Y})\)
type: Item
instance of: scholarly article
title: Swartz type results for nuclear and multiple 1-summing bilinear operators on \(c_0(\mathcal {X})\times c_0(\mathcal {Y})\)
zbMATH Open document ID: 1343.47026
author: Gabriela Badea
author: Dumitrŭ Popa
published in: Positivity
publication date: 2015-09-22T00:00:00Z
review text: In the paper under review the authors present a certain ``natural'' bilinear versions of \textit{Ch. Swartz}'s theorem [Trans. Am. Math. Soc., 179, 123--132 (1973; Zbl 0226.46038)] for bilinear operators on \(c_0(\mathcal{X})\), where \({\mathcal X} = (X_n)_{n=1}^\infty\) is a sequence of Banach spaces, and focus their attention to the validity of this theorem for nuclear and multiple \(1\)-summing bilinear operators. First they give some characterizations and examples of certain types of nuclear and multiple \(1\)-summing bilinear operators on these spaces, emphasizing the different behavior of the two classes. Here it is worth mentioning that, on \(c_0\), the class of nuclear operators coincide with those being multiple \(1\)-summing. They prove this is not true on \(c_0(\mathcal{X})\). Finally it is shown that this bilinear version of the Swartz's theorem fails for multiple \(1\)-summing bilinear operators.
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 47L20
Mathematics Subject Classification ID: 46B45
zbMATH DE Number: 6484280
zbMATH Keywords: multiple 1-summing bilinear operators
zbMATH Keywords: nuclear operators
zbMATH Keywords: Swartz's theorem
reviewed by: Jamilson Ramos Campos
MaRDI profile type: Publication
full work available at URL: s11117-014-0310-8
OpenAlex ID: W2035497768
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DOI: 10.1007/S11117-014-0310-8
description: scientific article; zbMATH DE number 6484280