Equivalence, unconditionality and convergence a.e. of the spline bases in spaces
Z. Ciesielski (1979)
Banach Center Publications
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Z. Ciesielski (1979)
Banach Center Publications
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Z. Ciesielski, T. Figiel (1983)
Studia Mathematica
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Stanisław Ropela (1979)
Banach Center Publications
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Z. Ciesielski (1975)
Studia Mathematica
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Jerzy Ryll (1978)
Studia Mathematica
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P. Wojtaszczyk (1973)
Studia Mathematica
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I. Singer (1968)
Studia Mathematica
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A. Pełczyński, I. Singer (1964)
Studia Mathematica
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A. Pełczyński (1969)
Studia Mathematica
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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 . We also give some positive results including a simpler proof that has a unique unconditional basis and a proof that has a unique unconditional basis when , and remains bounded.
Alfred Andrew (1979)
Studia Mathematica
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C. Leránoz (1992)
Studia Mathematica
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We prove that if 0 < p < 1 then a normalized unconditional basis of a complemented subspace of must be equivalent to a permutation of a subset of the canonical unit vector basis of . In particular, has unique unconditional basis up to permutation. Bourgain, Casazza, Lindenstrauss, and Tzafriri have previously proved the same result for .