擬相似之弱收縮變換

Abstract

Let T be a completely non-unitary (c.n.u.) weak contraction (in the sense of Sz. -Nagy and Foias). We show that T is quasi-similar to the direct sum of its C0 part and C11 part. As a corollary, two c.n.u. weak contractions are quasi- similar to each other if and only if their C0 parts and C11 parts are quasi-similar to each other, respectively. We also completely determine when c.n.u. weak contractions and C0 contractions are quasi-similar to normal operators.