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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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00029939_v138_n4_p1415_Boyd |
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todo:paper_00029939_v138_n4_p1415_Boyd2023-10-03T13:55:11Z Extreme and exposed points of spaces of integral polynomials Boyd, C. Lassalle, S. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 Boyd, C. Lassalle, S. 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. |
| format |
JOUR |
| author |
Boyd, C. Lassalle, S. |
| author_facet |
Boyd, C. Lassalle, S. |
| author_sort |
Boyd, C. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_00029939_v138_n4_p1415_Boyd |
| work_keys_str_mv |
AT boydc extremeandexposedpointsofspacesofintegralpolynomials AT lassalles extremeandexposedpointsofspacesofintegralpolynomials |
| _version_ |
1807323156532166656 |