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Ideals of homogeneous polynomials and weakly compact approximation property in Banach spaces
Authors:Erhan Çalişkan
Institution:(1) Faculty of Sciences and Arts, Department of Mathematics, Yıldız Technical University, Davutpaşa, 34210 Esenler İstanbul, Turkey
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
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