On Banach spaces with unconditional bases |
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Authors: | Wolfgang Lusky |
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Institution: | 1.Institute for Mathematics,University of Paderborn,Paderborn,Germany |
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Abstract: | LetX be a Banach space with a sequence of linear, bounded finite rank operatorsR
n:X→X such thatR
nRm=Rmin(n,m) ifn≠m and lim
n→∞
R
n
x=x for allx∈X. We prove that, ifR
n−Rn
−1 factors uniformly through somel
p and satisfies a certain additional symmetry condition, thenX has an unconditional basis. As an application, we study conditions on Λ ⊂ ℤ such thatL
Λ=closed span
, where
, has an unconditional basis. Examples include the Hardy space
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Keywords: | |
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