Subspaces of ℓ₂(X) and Rad(X) without local unconditional structure

Ryszard A. Komorowski, and Nicole Tomczak-Jaegermann. "Subspaces of ℓ₂(X) and Rad(X) without local unconditional structure." Studia Mathematica 149.1 (2002): 1-21. <http://eudml.org/doc/284885>.

@article{RyszardA2002,
abstract = {It is shown that if a Banach space X is not isomorphic to a Hilbert space then the spaces ℓ₂(X) and Rad(X) contain a subspace Z without local unconditional structure, and therefore without an unconditional basis. Moreover, if X is of cotype r < ∞, then a subspace Z of ℓ₂(X) can be constructed without local unconditional structure but with 2-dimensional unconditional decomposition, hence also with basis.},
author = {Ryszard A. Komorowski, Nicole Tomczak-Jaegermann},
journal = {Studia Mathematica},
keywords = {isomorphic characterization of Hilbert spaces; local unconditional structure},
language = {eng},
number = {1},
pages = {1-21},
title = {Subspaces of ℓ₂(X) and Rad(X) without local unconditional structure},
url = {http://eudml.org/doc/284885},
volume = {149},
year = {2002},
}

TY - JOUR
AU - Ryszard A. Komorowski
AU - Nicole Tomczak-Jaegermann
TI - Subspaces of ℓ₂(X) and Rad(X) without local unconditional structure
JO - Studia Mathematica
PY - 2002
VL - 149
IS - 1
SP - 1
EP - 21
AB - It is shown that if a Banach space X is not isomorphic to a Hilbert space then the spaces ℓ₂(X) and Rad(X) contain a subspace Z without local unconditional structure, and therefore without an unconditional basis. Moreover, if X is of cotype r < ∞, then a subspace Z of ℓ₂(X) can be constructed without local unconditional structure but with 2-dimensional unconditional decomposition, hence also with basis.
LA - eng
KW - isomorphic characterization of Hilbert spaces; local unconditional structure
UR - http://eudml.org/doc/284885
ER -