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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2010
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| 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 |
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| Sumario: | 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. |
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