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Title: Product spaces generated by bilinear maps and duality (English)
Author: Sánchez Pérez, Enrique A.
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 65
Issue: 3
Year: 2015
Pages: 801-817
Summary lang: English
Category: math
Summary: In this paper we analyse a definition of a product of Banach spaces that is naturally associated by duality with a space of operators that can be considered as a generalization of the notion of space of multiplication operators. This dual relation allows to understand several constructions coming from different fields of functional analysis that can be seen as instances of the abstract one when a particular product is considered. Some relevant examples and applications are shown, regarding pointwise products of Banach function spaces, spaces of integrable functions with respect to vector measures, spaces of operators, multipliers on Banach spaces of analytic functions and spaces of Lipschitz functions. (English)
Keyword: Banach space
Keyword: product
Keyword: multiplication operator
Keyword: duality
Keyword: Banach function space
Keyword: Hadamard product
Keyword: Lipschitz map
Keyword: integration
Keyword: vector measure
MSC: 46A32
MSC: 46B10
MSC: 46E30
MSC: 47A30
idZBL: Zbl 06537693
idMR: MR3407606
DOI: 10.1007/s10587-015-0209-y
Date available: 2015-10-04T18:21:13Z
Last updated: 2017-10-02
Stable URL:
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