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Property ( 𝐰𝐋 ) and the reciprocal Dunford-Pettis property in projective tensor products

Ioana Ghenciu (2015)

Commentationes Mathematicae Universitatis Carolinae

A Banach space X has the reciprocal Dunford-Pettis property ( R D P P ) if every completely continuous operator T from X to any Banach space Y is weakly compact. A Banach space X has the R D P P (resp. property ( w L ) ) if every L -subset of X * is relatively weakly compact (resp. weakly precompact). We prove that the projective tensor product X ⊗ π Y has property ( w L ) when X has the R D P P , Y has property ( w L ) , and L ( X , Y * ) = K ( X , Y * ) .

Property (wM*) and the unconditional metric compact approximation property

Ăsvald Lima (1995)

Studia Mathematica

The main objective of this paper is to give a simple proof for a larger class of spaces of the following theorem of Kalton and Werner. (a) X has property (M*), and (b) X has the metric compact approximation property Our main tool is a new property (wM*) which we show to be closely related to the unconditional metric approximation property.

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