Ideals of homogeneous polynomials and weakly compact approximation property in Banach spaces

Erhan Çalışkan

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 2, page 763-776
  • ISSN: 0011-4642

Abstract

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We show that a Banach space E has the weakly compact approximation property if and only if each continuous Banach-valued polynomial on E can be uniformly approximated on compact sets by homogeneous polynomials which are members of the ideal of homogeneous polynomials generated by weakly compact linear operators. An analogous result is established also for the compact approximation property.

How to cite

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Çalışkan, Erhan. "Ideals of homogeneous polynomials and weakly compact approximation property in Banach spaces." Czechoslovak Mathematical Journal 57.2 (2007): 763-776. <http://eudml.org/doc/31161>.

@article{Çalışkan2007,
abstract = {We show that a Banach space $E$ has the weakly compact approximation property if and only if each continuous Banach-valued polynomial on $E$ can be uniformly approximated on compact sets by homogeneous polynomials which are members of the ideal of homogeneous polynomials generated by weakly compact linear operators. An analogous result is established also for the compact approximation property.},
author = {Çalışkan, Erhan},
journal = {Czechoslovak Mathematical Journal},
keywords = {compact approximation property; weakly compact approximation property; ideals of homogeneous polynomials; compact approximation property; weakly compact approximation property; ideals of homogeneous polynomials},
language = {eng},
number = {2},
pages = {763-776},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Ideals of homogeneous polynomials and weakly compact approximation property in Banach spaces},
url = {http://eudml.org/doc/31161},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Çalışkan, Erhan
TI - Ideals of homogeneous polynomials and weakly compact approximation property in Banach spaces
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 2
SP - 763
EP - 776
AB - We show that a Banach space $E$ has the weakly compact approximation property if and only if each continuous Banach-valued polynomial on $E$ can be uniformly approximated on compact sets by homogeneous polynomials which are members of the ideal of homogeneous polynomials generated by weakly compact linear operators. An analogous result is established also for the compact approximation property.
LA - eng
KW - compact approximation property; weakly compact approximation property; ideals of homogeneous polynomials; compact approximation property; weakly compact approximation property; ideals of homogeneous polynomials
UR - http://eudml.org/doc/31161
ER -

References

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