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Density conditions in Fréchet and (DF)-spaces.

Klaus-Dieter. Bierstedt, José Bonet (1989)

Revista Matemática de la Universidad Complutense de Madrid

We survey our main results on the density condition for Fréchet spaces and on the dual density condition for (DF)-spaces (cf. Bierstedt and Bonet (1988)) as well as some recent developments.

Descriptive properties of elements of biduals of Banach spaces

Pavel Ludvík, Jiří Spurný (2012)

Studia Mathematica

If E is a Banach space, any element x** in its bidual E** is an affine function on the dual unit ball B E * that might possess a variety of descriptive properties with respect to the weak* topology. We prove several results showing that descriptive properties of x** are quite often determined by the behaviour of x** on the set of extreme points of B E * , generalizing thus results of J. Saint Raymond and F. Jellett. We also prove a result on the relation between Baire classes and intrinsic Baire classes...

Deviation from weak Banach–Saks property for countable direct sums

Andrzej Kryczka (2015)

Annales UMCS, Mathematica

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 (Xν) 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(Xν) is equal to the supremum of such deviations attained on the coordinates Xν. This is a quantitative version for operators of the result...

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