Czechoslovak Mathematical Journal, Vol. 57, No. 2, pp. 763-776, 2007

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

Erhan Caliskan

Erhan Caliskan, Yildiz Technical University, Faculty of Sciences and Arts, Department of Mathematics, Davutpasa, 34210 Esenler, Istanbul, Turkey, e-mail:

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.

Keywords: compact approximation property, weakly compact approximation property, ideals of homogeneous polynomials

Classification (MSC 2000): 46G20, 46B28, 46G25, 47B10

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