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Unconditional bases in countable- $ \mathcal{L}_1$ spaces


Author: J. C. Díaz
Journal: Proc. Amer. Math. Soc. 106 (1989), 357-363
MSC: Primary 46A35; Secondary 46A12
MathSciNet review: 931728
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Abstract: In this paper, we show that a countably- $ {\mathcal{L}_1}$ space which has an unconditional basis is isomorphic to some echelon sequence space of order 1. As a consequence, a countably- $ {\mathcal{L}_1}$ space with a basis is nuclear if all its bases are unconditional (this gives a partial answer to a conjecture of Wojtynski). We also study those countably- $ {\mathcal{L}_1}$ spaces on which a Fréchet lattice structure can be defined.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0931728-8
Article copyright: © Copyright 1989 American Mathematical Society