Extremal properties of the set of vector-valued Banach limits

• Autorzy: Francisco Javier García-Pacheco
• Języki publikacji: EN

Abstrakty

EN

In this manuscript we find another class of real Banach spaces which admit vector-valued Banach limits different from the classes found in [6, 7]. We also characterize the separating subsets of ℓ∞(X). For this we first need to study when the space of almost convergent sequences is closed in the space of bounded sequences, which turns out to happen only when the underlying space is complete. Finally, a study on the extremal structure of the set of vector-valued Banach limits is conducted when the underlying normed space is a Hilbert space.We also reach the conclusion that the set of vector-valued Banach limits is not a convex component of BCL(ℓ∞(X),X), provided that X is a 1-injective Banach space satisfying that the underlying compact Hausdorff topological space has isolated points.

Słowa kluczowe

EN

Banach limit; Almost convergence; Group of Isometries; Extremal Structure

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

otrzymano

2015-06-23

zaakceptowano

2015-10-16

online

2015-11-03

Twórcy

autor

Francisco Javier García-Pacheco

• Department of Mathematics, University of Cadiz, Puerto Real 11510, Spain

Bibliografia

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Identyfikatory

DOI

10.1515/math-2015-0067