Paper Title:

Banach-Saks Property and the Degree of Nondensifiability

Author(s):

Olivier de La Grandville

Departamento de Matemáticas,
Universidad Nacional de Educación a Distancia (UNED),
CL. Candalix s/n, 03202 Elche, Alicante,
Spain.
E-mail: gonzalogarciamacias@gmail.com

Abstract:

We present new upper bounds based on the so-called degree of nondensifiability (DND), for some quantification (see the references and definitions in the paper) of the Banach--Saks property. To be more precise, we prove that the mentioned quantification of a bounded subset of a Banach space can be bounded above by the DND of the convex hull of such a subset, multiplied by a constant. As a consequence of our main result, we derive an upper bound for the Banach-Saks property of bounded linear operators between Banach spaces. Through several examples, we show that such bounds are the best possible.

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