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The characteristic of weak convergence on Banach sequence lattices.

Baoxiang Wang, Tingfu Wang (1997)

Collectanea Mathematica

A sufficient and necessary condition for weak convergence of sequences in a class of Banach sequence lattices is obtained. As a direct application, a complete criterion of a weak convergence of sequences in l infinity is formulated.

The fixed point property in Musielak-Orlicz sequence spaces

Harold Bevan Thompson, Yunan Cui (2001)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we give necessary and sufficient conditions for a point in a Musielak-Orlicz sequence space equipped with the Orlicz norm to be an H-point. We give necessary and sufficient conditions for a Musielak-Orlicz sequence space equipped with the Orlicz norm to have the Kadec-Klee property, the uniform Kadec-Klee property and to be nearly uniformly convex. We show that a Musielak-Orlicz sequence space equipped with the Orlicz norm has the fixed point property if and only if it is reflexive....

The lattice copies of 1 in Banach lattices

Marek Wójtowicz (2001)

Commentationes Mathematicae Universitatis Carolinae

It is known that a Banach lattice with order continuous norm contains a copy of 1 if and only if it contains a lattice copy of 1 . The purpose of this note is to present a more direct proof of this useful fact, which extends a similar theorem due to R.C. James for Banach spaces with unconditional bases, and complements the c 0 - and -cases considered by Lozanovskii, Mekler and Meyer-Nieberg.

The problem of complementability for some spaces of vector measures of bounded variation with values in Banach spaces containing copies of c 0

L. Drewnowski, G. Emmanuele (1993)

Studia Mathematica

Let (S, ∑, m) be any atomless finite measure space, and X any Banach space containing a copy of c 0 . Then the Bochner space L 1 ( m ; X ) is uncomplemented in ccabv(∑,m;X), the Banach space of all m-continuous vector measures that are of bounded variation and have a relatively compact range; and ccabv(∑,m;X) is uncomplemented in cabv(∑,m;X). It is conjectured that this should generalize to all Banach spaces X without the Radon-Nikodym property.

The property ( β ) of Orlicz-Bochner sequence spaces

Paweł Kolwicz (2001)

Commentationes Mathematicae Universitatis Carolinae

A characterization of property ( β ) of an arbitrary Banach space is given. Next it is proved that the Orlicz-Bochner sequence space l Φ ( X ) has the property ( β ) if and only if both spaces l Φ and X have it also. In particular the Lebesgue-Bochner sequence space l p ( X ) has the property ( β ) iff X has the property ( β ) . As a corollary we also obtain a theorem proved directly in [5] which states that in Orlicz sequence spaces equipped with the Luxemburg norm the property ( β ) , nearly uniform convexity, the drop property and...

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