Unconditional bases in countable-ℒ₁ spaces

Díaz, J. C.

doi:10.1090/S0002-9939-1989-0931728-8

Unconditional bases in countable-$\mathcal {L}_1$ spaces
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by J. C. Díaz PDF

Proc. Amer. Math. Soc. 106 (1989), 357-363 Request permission

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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