Banas, Jozef; Martinón, Antonio Measures of weak noncompactness in Banach sequence spaces. (English) Zbl 0838.46015 Port. Math. 52, No. 2, 131-138 (1995). 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. Cited in 17 Documents MSC: 46B45 Banach sequence spaces 47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. Keywords:measure of weak noncompactness; Schur property; De Blasi measure PDFBibTeX XMLCite \textit{J. Banas} and \textit{A. Martinón}, Port. Math. 52, No. 2, 131--138 (1995; Zbl 0838.46015) Full Text: EuDML