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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: Camil Muscalu
Journal: Proc. Amer. Math. Soc. 125 (1997), 541-546
MSC (1991): Primary 47B10, 47B35
MathSciNet review: 1363434
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03714-3
PII: S 0002-9939(97)03714-3
Keywords: Lacunary Fourier series, Measurable operators
Received by editor(s): September 5, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society