Displaying similar documents to “On the H -property of some Banach sequence spaces”

The property ( β ) of Orlicz-Bochner sequence spaces

Paweł Kolwicz (2001)

Commentationes Mathematicae Universitatis Carolinae

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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...

On infinite dimensional uniform smoothness of Banach spaces

Stanisław Prus (1999)

Commentationes Mathematicae Universitatis Carolinae

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An infinite dimensional counterpart of uniform smoothness is studied. It does not imply reflexivity, but we prove that it gives some l p -type estimates for finite dimensional decompositions, weak Banach-Saks property and the weak fixed point property.