Radial limit of lacunary Fourier series with coefficients in non-commutative symmetric spaces
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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.References
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Additional Information
- Camil Muscalu
- Affiliation: Institute of Mathematics of the Romanian Academy, RO70700, PO Box 1-764, Buch- arest, Romania
- Address at time of publication: Department of Mathematics, Brown University, Providence, Rhode Island 02912
- Email: muscalu@stoilow.imar.ro, camil@gauss.math.brown.edu
- Received by editor(s): September 5, 1995
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 541-546
- MSC (1991): Primary 47B10, 47B35
- DOI: https://doi.org/10.1090/S0002-9939-97-03714-3
- MathSciNet review: 1363434