Some Properties of the Injective Tensor Product of Banach Spaces  

作　　者：Xiao Ping XUE Yong Jin LI Qing Ying BU(Qingying BU) 

机构地区：[1]Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P. R. China [2]Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, P. R. China [3]Department of Mathematics, University of Mississippi, University, MS 38677, USA

出　　处：《Acta Mathematica Sinica,English Series》2007年第9期1697-1706,共10页数学学报（英文版）

基　　金：the National Natural Science Foundation of China,Grant No.10571035

摘　　要：Let X and Y be Banach spaces such that X has an unconditional basis. Then X Y, the injective tensor product of X and Y, has the Radon-Nikodym property （respectively, the analytic Radon-Nikodym property, the near Radon-Nikodym property, non-containment of a copy of co, weakly sequential completeness） if and only if both X and Y have the same property and each continuous linear operator from the predual of X to Y is compact.Let X and Y be Banach spaces such that X has an unconditional basis. Then X Y, the injective tensor product of X and Y, has the Radon-Nikodym property （respectively, the analytic Radon-Nikodym property, the near Radon-Nikodym property, non-containment of a copy of co, weakly sequential completeness） if and only if both X and Y have the same property and each continuous linear operator from the predual of X to Y is compact.

关 键 词：tensor products types of Radon-Nikodym properties Schauder decomposition 

分 类 号：O185[理学—数学]