98-184 S.Ferleger

RUC-systems in non-commutative symmetric spaces. (27K, LATeX 2e) 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 RUC-basis. The aim of the article is to present a general procedure of constructing of RUC-bases in symmetric operator spaces associated with different von Neumann algebras $M$, in particular, with hyperfinite factor of type $II_1$.

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