The invariant subspace problem for bi-expansive operators in Krein spaces

Abstract

The invariant subspace problem is one of the most classical questions in operator theory and has attracted research studies for several years. The solutions for this question exist for compact operators. Recently, this question has been solved for bi-ontractive operators defined on a Krein space. The authors established that every bi-contractive operators defined on a Krein space, has maximal semi-definite invariant sub-spaces. In this paper, we address this question for bi-expansive operators defined on a Krein space using Riesz projection and fixed fundamental decomposition. We established that every bi-expansive operator defined on a Krein space has maximal invariant sub-spaces.