1Dipartimento di Matematica Facoltà di Scienze Università di Catania Viale Andrea Doria 6 95125 Catania, Italy 2Departamento de Matemática Aplicada ETS de Ingenieros Industriales Universidad Politécnica de Madrid C. José Gutiérrez Abascal 2 28006 Madrid, Spain
Studia Mathematica, Tome 169 (2005) no. 3, pp. 229-241
We show that a Banach space $X$ is an ${\scr L}_1$-space
(respectively, an ${\scr L}_\infty$-space) if and only if it
has the lifting (respectively, the extension) property for
polynomials which are weakly continuous on bounded sets. We also
prove that $X$ is an ${\scr L}_1$-space if and only if the
space ${\cal P}_{{\rm wb}}(^m\!X)$ of $m$-homogeneous scalar-valued polynomials on $X$
which are weakly continuous on bounded sets is an ${\scr
L}_\infty$-space.
Keywords:
banach space scr space respectively scr infty space only has lifting respectively extension property polynomials which weakly continuous bounded sets prove scr space only space cal m homogeneous scalar valued polynomials which weakly continuous bounded sets scr infty space
Affiliations des auteurs :
Raffaella Cilia
1
;
Joaquín M. Gutiérrez
2
1
Dipartimento di Matematica Facoltà di Scienze Università di Catania Viale Andrea Doria 6 95125 Catania, Italy
2
Departamento de Matemática Aplicada ETS de Ingenieros Industriales Universidad Politécnica de Madrid C. José Gutiérrez Abascal 2 28006 Madrid, Spain
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author = {Raffaella Cilia and Joaqu{\'\i}n M. Guti\'errez},
title = {Extension and lifting of weakly continuous polynomials},
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AU - Joaquín M. Gutiérrez
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Raffaella Cilia; Joaquín M. Gutiérrez. Extension and lifting of weakly continuous polynomials. Studia Mathematica, Tome 169 (2005) no. 3, pp. 229-241. doi: 10.4064/sm169-3-2
