Deviation from weak Banach–Saks property for countable direct sums

• Autorzy: Andrzej Kryczka
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

• Wydawca: Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
• Czasopismo: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
• Rocznik: 2014
• Tom: 68
• Numer: 2

Daty

wydano

2014

online

2015-05-23

Twórcy

autor

Andrzej Kryczka

Bibliografia

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Identyfikatory

DOI

10.17951/a.2014.68.2.51