M-Structures in vector-valued polynomial spaces

This paper is concerned with the study of M-structures in spaces of polynomials. More precisely, we discuss for E and F Banach spaces, whether the class of weakly continuous on bounded sets n-homogeneous polynomials, p w( nE, F), is an M-ideal in the space of continuous n-homogeneous polynomials p(...

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Autores principales: Dimant, Verónica, Lassalle, Silvia Beatriz
Publicado: 2012
Materias:
Homogeneous polynomials
M-ideals
Weakly continuous on bounded sets polynomials
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09446532_v19_n3_p685_Dimant
http://hdl.handle.net/20.500.12110/paper_09446532_v19_n3_p685_Dimant
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_09446532_v19_n3_p685_Dimant
record_format dspace
spelling paper:paper_09446532_v19_n3_p685_Dimant2023-06-08T15:53:49Z M-Structures in vector-valued polynomial spaces Dimant, Verónica Lassalle, Silvia Beatriz Homogeneous polynomials M-ideals Weakly continuous on bounded sets polynomials This paper is concerned with the study of M-structures in spaces of polynomials. More precisely, we discuss for E and F Banach spaces, whether the class of weakly continuous on bounded sets n-homogeneous polynomials, p w( nE, F), is an M-ideal in the space of continuous n-homogeneous polynomials p( nE,F). We show that there is some hope for this to happen only for a finite range of values of n. We establish sufficient conditions under which the problem has positive and negative answers and use the obtained results to study the particular cases when E = l pand F = l q or F is a Lorentz sequence space d(w,q). We extend to our setting the notion of property (M) introduced by Kalton which allows us to lift M-structures from the linear to the vector-valued polynomial context. Also, when p w( nE,F) is an M-ideal in p( nE, F) we prove a Bishop-Phelps type result for vector-valued polynomials and relate norm-attaining polynomials with farthest points and remotal sets. © Heldermann Verlag. Fil:Dimant, V. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Lassalle, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09446532_v19_n3_p685_Dimant http://hdl.handle.net/20.500.12110/paper_09446532_v19_n3_p685_Dimant
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Homogeneous polynomials
M-ideals
Weakly continuous on bounded sets polynomials
spellingShingle Homogeneous polynomials
M-ideals
Weakly continuous on bounded sets polynomials
Dimant, Verónica
Lassalle, Silvia Beatriz
M-Structures in vector-valued polynomial spaces
topic_facet Homogeneous polynomials
M-ideals
Weakly continuous on bounded sets polynomials
description This paper is concerned with the study of M-structures in spaces of polynomials. More precisely, we discuss for E and F Banach spaces, whether the class of weakly continuous on bounded sets n-homogeneous polynomials, p w( nE, F), is an M-ideal in the space of continuous n-homogeneous polynomials p( nE,F). We show that there is some hope for this to happen only for a finite range of values of n. We establish sufficient conditions under which the problem has positive and negative answers and use the obtained results to study the particular cases when E = l pand F = l q or F is a Lorentz sequence space d(w,q). We extend to our setting the notion of property (M) introduced by Kalton which allows us to lift M-structures from the linear to the vector-valued polynomial context. Also, when p w( nE,F) is an M-ideal in p( nE, F) we prove a Bishop-Phelps type result for vector-valued polynomials and relate norm-attaining polynomials with farthest points and remotal sets. © Heldermann Verlag.
author Dimant, Verónica
Lassalle, Silvia Beatriz
author_facet Dimant, Verónica
Lassalle, Silvia Beatriz
author_sort Dimant, Verónica
title M-Structures in vector-valued polynomial spaces
title_short M-Structures in vector-valued polynomial spaces
title_full M-Structures in vector-valued polynomial spaces
title_fullStr M-Structures in vector-valued polynomial spaces
title_full_unstemmed M-Structures in vector-valued polynomial spaces
title_sort m-structures in vector-valued polynomial spaces
publishDate 2012
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09446532_v19_n3_p685_Dimant
http://hdl.handle.net/20.500.12110/paper_09446532_v19_n3_p685_Dimant
work_keys_str_mv AT dimantveronica mstructuresinvectorvaluedpolynomialspaces
AT lassallesilviabeatriz mstructuresinvectorvaluedpolynomialspaces
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