 98184 S.Ferleger
 RUCsystems in noncommutative symmetric spaces.
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Mar 11, 98

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Abstract. Let $r_i \in \{0,1\}$, $i=0,\ldots$ be a sequence of independent random
variables. A biorthogonal system $(x_n, x^*_n)$ in a Banach space
X is called a RUC (an abbreviation for random unconditional convergence) if
for every $z$ from the closed linear hull of the
system the series $$\sum \epsilon _{_{i}}(\omega )\alpha _{_{i}}x_{_{i}}$$
converges for almost all $\omega \in \Omega $. If the system $(x_{_{n}})$
forms (Schauder) basis,
then it is called RUCbasis.
The aim of the article is to present a general procedure of constructing of
RUCbases in symmetric operator spaces associated with different von Neumann
algebras $M$, in particular, with hyperfinite factor of type $II_1$.
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