Title：Similarity Invariants of Geometric Operators

Abstract: In 1978, I.M.Cowen and R.G .Douglas introduced a class of geometric operators in a Grassmann manifold. In their influential paper they give a unitary invariant involving geometric ideas, such as curvature, that completely classifies these operators. At the same time they ask: Can one use geometric ideas to characterize completely the similarity invariants of geometric operators? We give a partial answer to this question. We show that the curvature and second fundamental form completely characterize the similarity invariants for a norm dense class of all geometric operators.