Uniqueness of unconditional basis
of $\ell _{p}(c_{0})$ and $\ell _{p}(\ell _{2})$, $0 p 1$
Studia Mathematica, Tome 150 (2002) no. 1, pp. 35-52
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We prove that the quasi-Banach spaces $\ell _{p}(c_{0})$ and $\ell _{p}(\ell _{2})$
($0 p 1$) have a unique unconditional basis up to permutation. Bourgain, Casazza, Lindenstrauss and Tzafriri have previously proved that the same is true for the respective Banach envelopes $\ell _{1}(c_{0})$ and $\ell _{1}(\ell _{2})$. They used duality techniques which are not available in the non-locally convex case.
Keywords:
prove quasi banach spaces ell ell ell have unique unconditional basis permutation bourgain casazza lindenstrauss tzafriri have previously proved respective banach envelopes ell ell ell duality techniques which available non locally convex
Affiliations des auteurs :
F. Albiac 1 ; C. Leránoz 1
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title = {Uniqueness of unconditional basis
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F. Albiac; C. Leránoz. Uniqueness of unconditional basis
of $\ell _{p}(c_{0})$ and $\ell _{p}(\ell _{2})$, $0< p< 1$. Studia Mathematica, Tome 150 (2002) no. 1, pp. 35-52. doi: 10.4064/sm150-1-4
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