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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access November 3, 2015

Extremal properties of the set of vector-valued Banach limits

  • Francisco Javier García-Pacheco
From the journal Open Mathematics

Abstract

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.

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Received: 2015-6-23
Accepted: 2015-10-16
Published Online: 2015-11-3

©2015 Francisco Javier García-Pacheco

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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