Product spaces generated by bilinear maps and duality

Czechoslovak Mathematical Journal

Enrique A. Sánchez Pérez¹ 

[1] Instituto Universitario de Matemática Pura y Aplicada (IUMPA), Universitat Politcnica de Valncia, Camino de Vera s/n, C.P. 46022 Valncia, Spain

关键词: Banach space;    product;    multiplication operator;    duality;    Banach function space;    Hadamard product;    Lipschitz map;    integration;    vector measure;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

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.

【 授权许可】

Unknown