Uniqueness of unconditional bases in c₀-products

1998/11/24 by Peter G. Casazza, Casazza, Peter G., Nigel J. Kalton +1
Mathematics · #46B07 #46B15 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46B07 #msc:46B15

paper · pdf · doi:10.48550/arxiv.math/9811145

23 pages; to appear: Studia Math

arxiv created 1998/11/24 · arxiv updated 2009/11/30

Abstract

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 c₀(X). In particular, we show that for Tsirelson's space T, every unconditional basis of c₀(T) must be equivalent to a subsequence of the canonical basis but c₀(T) still fails to have a unique unconditional basis. We also give some positive results including a simpler proof that c₀(l₁)has a unique unconditional basis.

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