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Measures of weak noncompactness in Banach sequence spaces. (English) Zbl 0838.46015
Summary: Based on a criterion for weak compactness in the \(\ell^p\) product of the sequence of Banach spaces \(E_i\), \(i= 1, 2,\dots\), we construct a measure of weak noncompactness in this space. It is shown that this measure is regular but not equivalent to the De Blasi measure of weak noncompactness provided the spaces \(E_i\) have the Schur property. Apart from this a formula for the De Blasi measure in the sequence space \(c_0(E_i)\) is also derived.

MSC:
46B45 Banach sequence spaces
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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