Invariant Subspaces of Operators on a Hilbert Space

Abstract

© 2020, PleiadesT Publishing,T Ltd. Abstract—In year 2006 the author proposed an approach to the invariant subspace problem for an operator on a Hilbert space, based on projection-convex combinations in C*-algebras with the unitary factorization property. In this paper, we present an operator inequality characterizing the invariant subspace of such an operator. Eight corollaries are obtained. For an operator C*-algebra A with a faithful trace, we give a sufficient condition of commutation for a partial isometry from A with a projection onto its invariant subspace.