 98188 Ferleger S.
 BASES IN (UMD)SPACES, APPLICATIONS TO THE NONCOMMUTATIVE SYMMETRIC SPACES
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Mar 11, 98

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Abstract. The present paper deals with the problems of existence of
Schauder
bases and unconditional finite dimensional decompositions (UFDD) in
some noncommutative symmetric spaces. In order to solve these
problems we study bases in arbitrary (UMD)spaces with strongly continuous
representations of compact abelian groups. It turns out that under
certain conditions the eigenvectors of such representations form
bases in (UMD)spaces while the eigenspaces form an unconditional
finite dimensional decompositions of the spaces. As an application, we
construct the first example of a Schauder basis in every operator $L_p$
space, $1<p<\infty$ associated with the hyperfinite von Neumann factor of
type $II_1.$
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