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.
@article{bwmeta1.element.ojs-doi-10_17951_a_2014_68_2_51,
author = {Andrzej Kryczka},
title = {Deviation from weak Banach--Saks property for countable direct sums},
journal = {Annales Universitatis Mariae Curie-Sk\l odowska, sectio A -- Mathematica},
volume = {68},
year = {2014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2014_68_2_51}
}
Andrzej Kryczka. Deviation from weak Banach–Saks property for countable direct sums. Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 68 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2014_68_2_51/
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