Unconditional bases in the Banach space L^p(2^\omega₁)
by
Magdalena Grzech
Politechnika Krakowska
Coauthors: Ryszard Frankiewicz, Ryszard Komorowski

P.Enflo and H.P. Rosenthal in [] considered a problem of existence of an unconditional basis in the Banach spaces L^p(\mu), where 1 < p < 0, p =/= 2, \mu is finite and dim(L^p(\mu) >= \aleph_\omega. They showed that such a space is not isomorphic to a subspace of a Banach space with an unconditional basis. By using a theorem of Maharam it can be reduced to the question of existence of unconditional basis in the space L^p(2^\kappa) for \kappa >= \aleph_\omega.

We prove that the space L^p(2^\kappa), for \kappa >= \aleph₁ has the same property.

References

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P. Enflo, H.P. Rosenthal Some results concerning L^p(\mu)-spaces, J. Functional Analysis 14, 325-348 (1973)

Date received: March 25, 2002