Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590926 | Journal of Functional Analysis | 2011 | 15 Pages |
Abstract
We study S-spaces and operators therein. An S-space is a Hilbert space with an additional inner product given by , where U is a unitary operator in . We investigate spectral properties of selfadjoint operators in S-spaces. We show that their spectrum is symmetric with respect to the real axis. As a main result we prove that for each selfadjoint operator A in an S-space we find an inner product which turns S into a Krein space and A into a selfadjoint operator therein. As a consequence we get a new simple condition for the existence of invariant subspaces of selfadjoint operators in Krein spaces, which provides a different insight into this well-know and in general unsolved problem.
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