Subspaces of $\ell _2(X)$ and ${\rm Rad}(X)$
without local unconditional structure
Studia Mathematica, Tome 149 (2002) no. 1, pp. 1-21
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
It is shown that if a Banach space $X$ is not isomorphic to a Hilbert space then the spaces $\ell _2(X)$ and $\mathop {\rm Rad}\nolimits (X)$ contain a subspace $Z$ without local unconditional structure, and therefore without an unconditional basis. Moreover, if $X$ is of cotype $r \infty $, then a subspace $Z$ of $\ell _2(X)$ can be constructed without local unconditional structure but with 2-dimensional unconditional decomposition, hence also with basis.
Keywords:
shown banach space isomorphic hilbert space spaces ell mathop rad nolimits contain subspace without local unconditional structure therefore without unconditional basis moreover cotype infty subspace ell constructed without local unconditional structure dimensional unconditional decomposition hence basis
Affiliations des auteurs :
Ryszard A. Komorowski 1 ; Nicole Tomczak-Jaegermann 2
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title = {Subspaces of $\ell _2(X)$ and ${\rm Rad}(X)$
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without local unconditional structure
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Ryszard A. Komorowski; Nicole Tomczak-Jaegermann. Subspaces of $\ell _2(X)$ and ${\rm Rad}(X)$
without local unconditional structure. Studia Mathematica, Tome 149 (2002) no. 1, pp. 1-21. doi: 10.4064/sm149-1-1
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