Uniqueness of unconditional bases in $c_0$-products

• Autorzy: P. G. Casazza , N. J. Kalton
• Języki publikacji: EN

Abstrakty

EN

We give counterexamples to a conjecture of Bourgain, Casazza, Lindenstrauss and Tzafriri that if X has a unique unconditional basis (up to permutation) then so does $c_0(X)$. We also give some positive results including a simpler proof that $c_0(ℓ_1)$ has a unique unconditional basis and a proof that $c_0(ℓ_{p_n}^{N_n})$ has a unique unconditional basis when $p_n ￬ 1$, $N_{n+1} ≥ 2N_{n}$ and $(p_n-p_{n+1}) logN_{n}$ remains bounded.

Kategorie tematyczne

• 46B15: Summability and bases
• 46B07: Local theory of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1999
• Tom: 133
• Numer: 3
• Strony: 275-294

Daty

wydano

1999

otrzymano

1998-05-15

Twórcy

autor

P. G. Casazza

• Department of Mathematics, University of Missouri, Columbia, Missouri 65211, U.S.A.

autor

N. J. Kalton

• Department of Mathematics, University of Missouri, Columbia, Missouri 65211, U.S.A.

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