A construction of basis in $C^{(1)}(I^{2})$

Z. Ciesielski

Displaying similar documents to “A construction of basis in $C^{(1)} (I^{2})$ ”

Some curious bases for $c_{0}$ and C[0,1]

J. Holub, J. Retherford (1970)

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Hilbertian, Besselian, and semi-shrinking bases

J. Holub (1971)

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Uniqueness of unconditional bases in $c_{0}$ -products

P. Casazza, N. Kalton (1999)

Studia Mathematica

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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 $p_{n} ￬ 1$ , $N_{n + 1} \geq 2 N_{n}$ and $(p_{n} - p_{n + 1}) l o g N_{n}$ remains bounded.