Articles

On some parameters related to weak noncompactness in L¹(μ,E)

Published in: Quaestiones Mathematicae
Volume 32 , issue 3, pages: 427–434

DOI: 10.2989/QM.2009.32.3.11.912

Author(s): Diana CaponettiDepartment of Mathematics, Italy,

Keywords: Bochner integrable function, weak compactness, w-tightness, measure of weak noncompactness,

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Abstract

A weak measure of noncompactness γU is defined in a Banach space in terms of convex compactness. We obtain relationships between the measure γU (A) of a bounded set A in the Bochner space L¹ (μ,E) and two parameters Π(A) and Δ₁(A). Then the criterion for relative weak compactness due to Ülger [19] and Diestel-Ruess-Schachermayer [11] is recovered.

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