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ISSN 1088-6826(e) ISSN 0002-9939(p)

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

Author(s): 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.

References:

[A]: J.Arazy., Some remarks on interpolation theorems and the boundedness of triangular projection in unitary matrix spaces, Int. Eq. and Op. Theory 1/4 (1978). MR 81k:47056a
[Bl]: O.Blasco., Boundary values of functions in vector valued Hardy spaces and geometry of Banach spaces, J.Func.Anal. 78 (1988), 346-364. MR 89f:46080
[BD]: A.V.Buchvalov, A.A.Danilevich., Boundary properties of analytic and harmonic functions with values in Banach spaces, Mat.Zametki 31 (1982). MR 84f:46032
[DU]: J.Diestel, J.J.Uhl., Vector measure, Providence, (1977).
[DDP1]: P.G.Doods, T.K.Doods, B. de Pagter., Non-commutative Banach function spaces, Math. Z 201 (1989), 583-597. MR 90j:46054
[DDP2]: -, Weakly compact subsets of symmetric operator spaces, Tech. rep., Delft University of Technology, (1990).
[D]: P.N.Dowling., Radon-Nikodym properties associated with subsets of countable discrete abelian groups, Trans.Amer.Math.Soc. 327 (1991), 879-890. MR 92a:46019
[E]: G.A.Edgar., Banach spaces with the analytic Radon Nikodym property and compact abelian groups, 1992.
[FK]: T.Fack, H. Kosaki., Generalised s-numbers of $\tau$ -measurable operators, Pacific J.Math. 123 (1986), 269-300. MR 87h:46122
[HP]: U.Haagerup, G.Pisier., Factorization of analytic functions with values in noncommutative $L_{1}$ -spaces and applications, Canad.J.Math 41 (1989), 882-906. MR 91g:46068
[LT]: J.Lindenstrauss, L.Tzafiri., Classical Banach spaces, Springer-Verlag, 2 (1979). MR 81c:46001
[M]: C.Muscalu., New results on interpolation in non-commutative analysis., preprint, (1995).
[N]: E.Nelson., Notes on non-commutative integration., J.Func. Anal. 15 (1974), 103-116. MR 50:8102
[SZ]: S.Stratila, L.Zsido., Lectures on Von Neumann algebras., Abacus Press (1979). MR 81j:46089
[X1]: Q.Xu., Analytic functions with values in lattices and symmetric spaces of measurable operators., Math.Proc.Camb.Phil.Soc. 109 (1991), 541-563. MR 92g:46036
[X2]: Q.Xu., Radon Nikodym property in symmetric spaces of measurable operators, Proc. Amer. Math. Soc 115 (1992), 329-335. MR 92i:46074

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