Product spaces generated by bilinear maps and duality
Czechoslovak Mathematical Journal (2015)
- Volume: 65, Issue: 3, page 801-817
- ISSN: 0011-4642
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topSánchez Pérez, Enrique A.. "Product spaces generated by bilinear maps and duality." Czechoslovak Mathematical Journal 65.3 (2015): 801-817. <http://eudml.org/doc/271808>.
@article{SánchezPérez2015,
abstract = {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.},
author = {Sánchez Pérez, Enrique A.},
journal = {Czechoslovak Mathematical Journal},
keywords = {Banach space; product; multiplication operator; duality; Banach function space; Hadamard product; Lipschitz map; integration; vector measure},
language = {eng},
number = {3},
pages = {801-817},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Product spaces generated by bilinear maps and duality},
url = {http://eudml.org/doc/271808},
volume = {65},
year = {2015},
}
TY - JOUR
AU - Sánchez Pérez, Enrique A.
TI - Product spaces generated by bilinear maps and duality
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 3
SP - 801
EP - 817
AB - 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.
LA - eng
KW - Banach space; product; multiplication operator; duality; Banach function space; Hadamard product; Lipschitz map; integration; vector measure
UR - http://eudml.org/doc/271808
ER -
References
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