THE INVARIANT SUBSPACE PROBLEM FOR CONTRACTIVE OPERATORS IN KREIN SPACES

Abstract

The invariant subspace problem, which is one of the most funda mental questions in operator theory and which has been a subject of study for several decades remains open even on a Hilbert space. However, for certain classes of operators, for example, compact operators, solutions do exist. In this paper, we address this question for contractive operators T defined on a Krein space K. We investigate the existence of semi-definite invariant subspaces and establish that every contractive operator T defined on a Krein space K has maximal semi-definite invariant subspaces