Deviation from weak Banach–Saks property for countable direct sums

Andrzej Kryczka

Abstract


We introduce a seminorm for bounded linear operators between Banach spaces that shows the deviation from the weak Banach–Saks property. We prove that if (Xv) is a sequence of Banach spaces and a Banach sequence lattice E has the Banach–Saks property, then the deviation from the weak Banach–Saks property of an operator of a certain class between direct sums E(Xv) is equal to the supremum of such deviations attained on the coordinates Xv. This is a quantitative version for operators of the result for the Köthe–Bochner sequence spaces E(X) that if E has the Banach–Saks property, then E(X) has the weak Banach–Saks property if and only if so has X.

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References


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DOI: http://dx.doi.org/10.17951/a.2014.68.2.51
Data publikacji: 2015-05-23 16:29:45
Data złożenia artykułu: 2015-05-09 13:33:31

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