Some remarks on the equality W ( E , F * ) = K ( E , F * )

Giovanni Emmanuele

Archivum Mathematicum (1998)

  • Volume: 034, Issue: 4, page 417-425
  • ISSN: 0044-8753

Abstract

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We show that the equality W ( E , F * ) = K ( E , F * ) is a necessary condition for the validity of certain results about isomorphic properties in the projective tensor product E ⊗ π F of two Banach spaces under some approximation property type assumptions.

How to cite

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Emmanuele, Giovanni. "Some remarks on the equality $W(E,F^\ast ) = K(E,F^\ast )$." Archivum Mathematicum 034.4 (1998): 417-425. <http://eudml.org/doc/248201>.

@article{Emmanuele1998,
abstract = {We show that the equality $W(E,F^\ast )=K(E,F^\ast )$ is a necessary condition for the validity of certain results about isomorphic properties in the projective tensor product $E \otimes _\pi F$ of two Banach spaces under some approximation property type assumptions.},
author = {Emmanuele, Giovanni},
journal = {Archivum Mathematicum},
keywords = {operator spaces; isomorphic properties; approximation properties; isomorphic properties; approximation properties; spaces of operators; projective tensor product; approximation property},
language = {eng},
number = {4},
pages = {417-425},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Some remarks on the equality $W(E,F^\ast ) = K(E,F^\ast )$},
url = {http://eudml.org/doc/248201},
volume = {034},
year = {1998},
}

TY - JOUR
AU - Emmanuele, Giovanni
TI - Some remarks on the equality $W(E,F^\ast ) = K(E,F^\ast )$
JO - Archivum Mathematicum
PY - 1998
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 034
IS - 4
SP - 417
EP - 425
AB - We show that the equality $W(E,F^\ast )=K(E,F^\ast )$ is a necessary condition for the validity of certain results about isomorphic properties in the projective tensor product $E \otimes _\pi F$ of two Banach spaces under some approximation property type assumptions.
LA - eng
KW - operator spaces; isomorphic properties; approximation properties; isomorphic properties; approximation properties; spaces of operators; projective tensor product; approximation property
UR - http://eudml.org/doc/248201
ER -

References

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  16. Classical Banach spaces, Sequence Spaces, EMG 92, Springer Verlag 1977. MR0500056
  17. Classical Banach spaces, Function Spaces, EMG 97, Springer Verlag 1979. MR0540367
  18. Produits tensoriels projectifs d’espaces de Banach, Colloquium Math. 36 (1976) 255-267. Zbl0356.46058MR0438153
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  22. The compact approximation property does not imply the approximation property, Studia Math. 103 (1992) 99-108. Zbl0814.46017MR1184105

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