Weyl type theorems for selfadjoint operators on Krein spaces

Abstract

In this paper, we introduce a notion of the $\mathcal{J}$-kernel of a bounded linear operator on a Krein space and study the $\mathcal{J}$-Fredholm theory for Krein space operators. Using $\mathcal{J}$-Fredholm theory, we discuss when $(a\text{-})\mathcal{J}$-Weyl's theorem or $(a\text{-})\mathcal{J}$-Browder's theorem holds for bounded linear operators on a Krein space instead of a Hilbert space.