Some Properties of the Injective Tensor Product of Banach Spaces



Let X and Y be Banach spaces such that X has an unconditional basis. Then X\( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{ \otimes } \)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 c0, 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.


tensor products types of Radon–Nikodym properties Schauder decomposition 

MR (2000) Subject Classification

46M05 46B28 


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© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  1. 1.Department of MathematicsHarbin Institute of TechnologyHarbinP. R. China
  2. 2.Department of MathematicsSun Yat-sen UniversityGuangzhouP. R. China
  3. 3.Department of MathematicsUniversity of MississippiUniversityUSA

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