Semi-embeddings and weakly sequential completeness of the projective tensor product

• Autorzy: Qingying Bu
• Języki publikacji: EN

Abstrakty

EN

We show that if ${P_{k}}$ is a boundedly complete, unconditional Schauder decomposition of a Banach space X, then X is weakly sequentially complete whenever $P_{k}X$ is weakly sequentially complete for each k ∈ ℕ. Then through semi-embeddings, we give a new proof of Lewis's result: if one of Banach spaces X and Y has an unconditional basis, then X ⊗̂ Y, the projective tensor product of X and Y, is weakly sequentially complete whenever both X and Y are weakly sequentially complete.

Kategorie tematyczne

• 46B22: Radon-Nikod{\'y}m, Kre{\u\i}n-Milman and related properties
• 46M05: Tensor products
• 46B28: Spaces of operators; tensor products; approximation properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 169
• Numer: 3
• Strony: 287-294

Daty

wydano

2005

Twórcy

autor

Qingying Bu

• Department of Mathematics, University of Mississippi, University, MS 38677, U.S.A.

Identyfikatory

DOI

10.4064/sm169-3-4