Deviation from weak Banach–Saks property for countable direct sums
Andrzej Kryczka (2014)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
Similarity:
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...