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

Ioana Ghenciu

Commentationes Mathematicae Universitatis Carolinae (2015)

  • Volume: 56, Issue: 3, page 319-329
  • ISSN: 0010-2628

Abstract

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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 * ) .

How to cite

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Ghenciu, Ioana. "Property $ \bf {(wL)}$ and the reciprocal Dunford-Pettis property in projective tensor products." Commentationes Mathematicae Universitatis Carolinae 56.3 (2015): 319-329. <http://eudml.org/doc/271640>.

@article{Ghenciu2015,
abstract = {A Banach space $X$ has the reciprocal Dunford-Pettis property ($RDPP$) if every completely continuous operator $T$ from $X$ to any Banach space $Y$ is weakly compact. A Banach space $X$ has the $RDPP$ (resp. property $(wL)$) if every $L$-subset of $X^*$ is relatively weakly compact (resp. weakly precompact). We prove that the projective tensor product $X \otimes \{_\pi \} Y$ has property $(wL)$ when $X$ has the $RDPP$, $Y$ has property $(wL)$, and $L(X,Y^*)=K(X,Y^*)$.},
author = {Ghenciu, Ioana},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {the reciprocal Dunford-Pettis property; property $(wL)$; spaces of compact operators; weakly precompact sets},
language = {eng},
number = {3},
pages = {319-329},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Property $ \bf \{(wL)\}$ and the reciprocal Dunford-Pettis property in projective tensor products},
url = {http://eudml.org/doc/271640},
volume = {56},
year = {2015},
}

TY - JOUR
AU - Ghenciu, Ioana
TI - Property $ \bf {(wL)}$ and the reciprocal Dunford-Pettis property in projective tensor products
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2015
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 56
IS - 3
SP - 319
EP - 329
AB - A Banach space $X$ has the reciprocal Dunford-Pettis property ($RDPP$) if every completely continuous operator $T$ from $X$ to any Banach space $Y$ is weakly compact. A Banach space $X$ has the $RDPP$ (resp. property $(wL)$) if every $L$-subset of $X^*$ is relatively weakly compact (resp. weakly precompact). We prove that the projective tensor product $X \otimes {_\pi } Y$ has property $(wL)$ when $X$ has the $RDPP$, $Y$ has property $(wL)$, and $L(X,Y^*)=K(X,Y^*)$.
LA - eng
KW - the reciprocal Dunford-Pettis property; property $(wL)$; spaces of compact operators; weakly precompact sets
UR - http://eudml.org/doc/271640
ER -

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