Portugaliæ Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 52, No. 2, pp. 131-138 (1995)

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Measures of Weak Noncompactness in Banach Sequence Spaces

Jozef Banas and Antonio Martinón

Department of Mathematics, Technical University of Rzeszów,
35-959 Rzeszów, W. Pola 2 - POLAND Department of Mathematical Analysis, University of La Laguna,
38271 La Laguna (Tenerife) - SPAIN

Abstract: Based on a criterion for weak compactness in the $\ell^p$ product of the sequence of Banach spaces $E_i$, $i = 1, 2, \ldots$, 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.

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