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

Qingying Bu. "Semi-embeddings and weakly sequential completeness of the projective tensor product." Studia Mathematica 169.3 (2005): 287-294. <http://eudml.org/doc/284705>.

@article{QingyingBu2005,
abstract = {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.},
author = {Qingying Bu},
journal = {Studia Mathematica},
keywords = {projective tensor product; semi-embedding; weak sequential completeness; unconditional Schauder decomposition},
language = {eng},
number = {3},
pages = {287-294},
title = {Semi-embeddings and weakly sequential completeness of the projective tensor product},
url = {http://eudml.org/doc/284705},
volume = {169},
year = {2005},
}

TY - JOUR
AU - Qingying Bu
TI - Semi-embeddings and weakly sequential completeness of the projective tensor product
JO - Studia Mathematica
PY - 2005
VL - 169
IS - 3
SP - 287
EP - 294
AB - 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.
LA - eng
KW - projective tensor product; semi-embedding; weak sequential completeness; unconditional Schauder decomposition
UR - http://eudml.org/doc/284705
ER -