论文信息 - OBSERVATIONS ABOUT THE PROJECTIVE TENSOR PRODUCT OF BANACH SPACES, I—

OBSERVATIONS ABOUT THE PROJECTIVE TENSOR PRODUCT OF BANACH SPACES, I—

Abstract A sequential description of the projective tensor product lp⊗X, is given. This description allows us to show the inclusion lp⊗X, into lp⊗X, is a semi-embedding. As a consequence, if X has the Radon-Nikodym property so does lp⊗X, A discussion of difficulties with Lp(0, 1) ⊗X, follows.

Joe Diestel | J. Diestel | Q. Bu | Qingying Bu

[1] C. Stegall. The duality between Asplund spaces and spaces with the Radon-Nikodym property , 1978 .

[2] D. R. Lewis. Duals of tensor products , 1977 .

[3] Joram Lindenstrauss,et al. Classical Banach spaces I: Sequence Spaces. , 1977 .

[4] A. Grothendieck. Résumé de la théorie métrique des produits tensoriels topologiques , 1996 .

[5] A. Grothendieck,et al. Sur Certaines Classes De Suites Dans Les Espaces De Banach, Et Le Théorème De Dvoretzky-Rogers (fac-simile, Boletim da Sociedade de Matemática de São Paulo, Vol. 8, 1958) , 1998 .

[6] Joram Lindenstrauss. Classical Banach Spaces II: Function Spaces , 1979 .

[7] Stefan Heinrich,et al. Applications of ultrapowers to the uniform and Lipschitz classification of Banach spaces , 1982 .

[8] J. Diestel,et al. Some observations about the space of weakly continuous functions , 1992 .

[9] J. Bourgain,et al. Applications of the theory of semi-embeddings to Banach space theory , 1983 .

[10] R. Phelps. Convex Functions, Monotone Operators and Differentiability , 1989 .

[11] Gilles Pisier,et al. Holomorphic semi-groups and the geometry of Banach spaces , 1982 .