Extreme and exposed points of spaces of integral polynomials

We show that if E is a real Banach space such that E′ has the approximation property and such that ℓ1 → ⊗ n,s,e,E, then the set of extreme points of the unit ball of PI (nE) is equal to {± Φn: Φ ∈ E′ ∥ Φ ∥ = 1}. Under the additional assumption that E′ has a countable norming set, we see that the set...

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Detalles Bibliográficos
Autor principal: Lassalle, Silvia Beatriz
Publicado: 2010
Materias:
Exposed points
Extreme points
Integral polynomials
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v138_n4_p1415_Boyd
http://hdl.handle.net/20.500.12110/paper_00029939_v138_n4_p1415_Boyd
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00029939_v138_n4_p1415_Boyd
record_format dspace
spelling paper:paper_00029939_v138_n4_p1415_Boyd2023-06-08T14:23:30Z Extreme and exposed points of spaces of integral polynomials Lassalle, Silvia Beatriz Exposed points Extreme points Integral polynomials We show that if E is a real Banach space such that E′ has the approximation property and such that ℓ1 → ⊗ n,s,e,E, then the set of extreme points of the unit ball of PI (nE) is equal to {± Φn: Φ ∈ E′ ∥ Φ ∥ = 1}. Under the additional assumption that E′ has a countable norming set, we see that the set of exposed points of the unit ball of PI(nE) is also equal to {± Φn Φisin; E′ ∥ Φ ∥ © 2009 American Mathematical Society. Fil:Lassalle, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2010 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v138_n4_p1415_Boyd http://hdl.handle.net/20.500.12110/paper_00029939_v138_n4_p1415_Boyd
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Exposed points
Extreme points
Integral polynomials
spellingShingle Exposed points
Extreme points
Integral polynomials
Lassalle, Silvia Beatriz
Extreme and exposed points of spaces of integral polynomials
topic_facet Exposed points
Extreme points
Integral polynomials
description We show that if E is a real Banach space such that E′ has the approximation property and such that ℓ1 → ⊗ n,s,e,E, then the set of extreme points of the unit ball of PI (nE) is equal to {± Φn: Φ ∈ E′ ∥ Φ ∥ = 1}. Under the additional assumption that E′ has a countable norming set, we see that the set of exposed points of the unit ball of PI(nE) is also equal to {± Φn Φisin; E′ ∥ Φ ∥ © 2009 American Mathematical Society.
author Lassalle, Silvia Beatriz
author_facet Lassalle, Silvia Beatriz
author_sort Lassalle, Silvia Beatriz
title Extreme and exposed points of spaces of integral polynomials
title_short Extreme and exposed points of spaces of integral polynomials
title_full Extreme and exposed points of spaces of integral polynomials
title_fullStr Extreme and exposed points of spaces of integral polynomials
title_full_unstemmed Extreme and exposed points of spaces of integral polynomials
title_sort extreme and exposed points of spaces of integral polynomials
publishDate 2010
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v138_n4_p1415_Boyd
http://hdl.handle.net/20.500.12110/paper_00029939_v138_n4_p1415_Boyd
work_keys_str_mv AT lassallesilviabeatriz extremeandexposedpointsofspacesofintegralpolynomials
_version_ 1768545260765446144

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