98-188 Ferleger S.

BASES IN (UMD)-SPACES, APPLICATIONS TO THE NON-COMMUTATIVE SYMMETRIC SPACES (79K, LaTeX 2e) Mar 11, 98

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

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 $II_1.$

Files: 98-188.tex