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