Asymptotically convex Banach spaces and The Index of Rotundity Problem

Asymptotically convex Banach spaces and The Index of Rotundity Problem

The Index of Rotundity Problem asks whether a Banach space which admits equivalent renormings with index of rotundity as small as desired also admits an equivalent rotund renorming. In this paper we continue the ongoing search for a negative answer to this question by making use of a new concept: as...

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Lenguaje:English
Publicado: Universidad Católica del Norte, Departamento de Matemáticas 2012
Materias:
Rotund
renorming
Banach space
Acceso en línea:http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172012000200001
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spelling oai:scielo:S0716-091720120002000012012-07-18Asymptotically convex Banach spaces and The Index of Rotundity Problem Rotund renorming Banach space The Index of Rotundity Problem asks whether a Banach space which admits equivalent renormings with index of rotundity as small as desired also admits an equivalent rotund renorming. In this paper we continue the ongoing search for a negative answer to this question by making use of a new concept: asymptotically convex Banach spaces. Some applications to The Approximation Hyperplane Series Property are given.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.31 n.2 20122012-06-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172012000200001en10.4067/S0716-09172012000200001
institution Scielo Chile
collection Scielo Chile
language English
topic Rotund
renorming
Banach space
spellingShingle Rotund
renorming
Banach space
Asymptotically convex Banach spaces and The Index of Rotundity Problem
description The Index of Rotundity Problem asks whether a Banach space which admits equivalent renormings with index of rotundity as small as desired also admits an equivalent rotund renorming. In this paper we continue the ongoing search for a negative answer to this question by making use of a new concept: asymptotically convex Banach spaces. Some applications to The Approximation Hyperplane Series Property are given.
title Asymptotically convex Banach spaces and The Index of Rotundity Problem
title_short Asymptotically convex Banach spaces and The Index of Rotundity Problem
title_full Asymptotically convex Banach spaces and The Index of Rotundity Problem
title_fullStr Asymptotically convex Banach spaces and The Index of Rotundity Problem
title_full_unstemmed Asymptotically convex Banach spaces and The Index of Rotundity Problem
title_sort asymptotically convex banach spaces and the index of rotundity problem
publisher Universidad Católica del Norte, Departamento de Matemáticas
publishDate 2012
url http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172012000200001
_version_ 1718439782547193856

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