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

100%

Bu Q.

Studia Mathematica

2005

tom 169

nr 3

287-294

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.

Diagonals of projective tensor products and orthogonally additive polynomials

63%

Bu Q., Buskes G.

Studia Mathematica

2014

tom 221

nr 2

101-115

Let E be a Banach space with 1-unconditional basis. Denote by $Δ(⊗̂_{n,π}E)$ (resp. $Δ(⊗̂_{n,s,π}E)$) the main diagonal space of the n-fold full (resp. symmetric) projective Banach space tensor product, and denote by $Δ(⊗̂_{n,|π|}E)$ (resp. $Δ(⊗̂_{n,s,|π|}E)$) the main diagonal space of the n-fold full (resp. symmetric) projective Banach lattice tensor product. We show that these four main diagonal spaces are pairwise isometrically isomorphic, and in addition, that they are isometrically lattice isomorphic to $E_{[n]}$, the completion of the n-concavification of E. Using these isometries, we also show that the norm of any (vector valued) continuous orthogonally additive homogeneous polynomial on E equals the norm of its associated symmetric linear operator.

Ograniczanie wyników

2 Studia Mathematica

2 Bu Q.

1 Buskes G.

1 2014

1 2005

Wyniki wyszukiwania

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

Diagonals of projective tensor products and orthogonally additive polynomials