Czechoslovak Mathematical Journal

, Volume 65, Issue 3, pp 801–817 | Cite as

Product spaces generated by bilinear maps and duality



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.


Banach space product multiplication operator duality Banach function space Hadamard product Lipschitz map integration vector measure 

MSC 2010

46A32 46E30 47A30 46B10 


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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2015

Authors and Affiliations

  1. 1.Instituto Universitario de Matemática Pura y Aplicada (IUMPA)Universitat Politècnica de ValènciaValènciaSpain

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