Weak sequential completeness of spaces of homogeneous polynomials

作者：Bu, Qingying^*; Ji, Donghai; Wong, Ngai-Ching

来源：Journal of Mathematical Analysis and Applications, 2015, 427(2): 1119-1130.

DOI：10.1016/j.jmaa.2015.02.078

• Homogeneous polynomials
• Weak sequential completeness
• Reflexivity

Let P-w(E-n; 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 P-w, (E-n; 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 P-w (E-n; F) are equivalent whenever both E and F are reflexive.

• 出版日期2015-7-15
• 单位哈尔滨学院; 中山大学