Geodesic
Extension and lifting of weakly continuous polynomials
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
Studia Mathematica, Tome 169 (2005) no. 3, pp. 229-241 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm169-3-2
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

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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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

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