Radial limit of lacunary Fourier series with coefficients in non-commutative symmetric spaces

Muscalu, Camil

doi:10.1090/S0002-9939-97-03714-3

Radial limit of lacunary Fourier series with coefficients in non-commutative symmetric spaces
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Proc. Amer. Math. Soc. 125 (1997), 541-546 Request permission

Abstract:

Let $E$ be a rearrangement invariant space, $\Lambda \subseteq {\mathbb {Z}}$ an arbitrary set and $(M,\tau )$ a von Neumann algebra with a semifinite normal faithful trace. It is proved that the associated symmetric space of measurable operators $E(M,\tau )$ has $\Lambda$-RNP if and only if $E$ has $\Lambda$-RNP extending in this way some previous results by Q. Xu.

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