98-188 Ferleger S.
BASES IN (UMD)-SPACES, APPLICATIONS TO THE NON-COMMUTATIVE SYMMETRIC SPACES (79K, LaTeX 2e) 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 non-commutative 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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