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

Published in: Quaestiones Mathematicae
Volume 32, issue 3, 2009 , pages: 427–434
DOI: 10.2989/QM.2009.
Author(s): Diana CaponettiDepartment of Mathematics, Italy


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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