Weak sequential completeness of spaces of homogeneous polynomials

Qingying Bu,Donghai Ji,Ngai-Ching Wong

doi:10.1016/j.jmaa.2015.02.078

Weak sequential completeness of spaces of homogeneous polynomials

Qingying Bu, Donghai Ji + Show 1 more

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https://doi.org/10.1016/j.jmaa.2015.02.078

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Journal: Journal of Mathematical Analysis and Applications	Publication Date: Mar 2, 2015
Citations: 17	License type: elsevier-specific: oa user license

Affiliation: National Sun Yat-sen University, University of Mississippi, Harbin University of Science and Technology

#Weak Sequential Completeness #Banach Space + Show 8 more

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Abstract

Let Pw(En;F) be the space of all continuous n-homogeneous polynomials from a Banach space E into another F, that are weakly continuous on bounded sets. We give sufficient conditions for the weak sequential completeness of Pw(En;F). These sufficient conditions are also necessary if both E⁎ and F have the bounded compact approximation property. We also show that the weak sequential completeness and the reflexivity of Pw(En;F) are equivalent whenever both E and F are reflexive.

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