Displaying similar documents to “Transitivity of the norm on Banach spaces.”

Characterizations of almost transitive superreflexive Banach spaces

Julio Becerra Guerrero, Angel Rodriguez Palacios (2001)

Commentationes Mathematicae Universitatis Carolinae

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Almost transitive superreflexive Banach spaces have been considered in [7] (see also [4] and [6]), where it is shown that such spaces are uniformly convex and uniformly smooth. We prove that convex transitive Banach spaces are either almost transitive and superreflexive (hence uniformly smooth) or extremely rough. The extreme roughness of a Banach space X means that, for every element u in the unit sphere of X , we have lim sup ∥ h ∥ → 0 ∥ u + h ∥ + ∥ u - h ∥ - 2 ∥ h ∥ = 2 . We note that, in general, the property of convex transitivity for...

Extremal properties of the set of vector-valued Banach limits

Francisco Javier García-Pacheco (2015)

Open Mathematics

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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...