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Via approximative eigensequences we introduce the notion of spectral points of type π+ and π- for self-adjoint operators in Krein spaces. They are stable under compact perturbations. For real spectral points of type π+ and π- which are not in the interior of the spectrum we prove that the growth of the resolvent in some neighbourhood of them is of finite order. There exists a local spectral function with singularities. It turns out that all spectral subspaces corresponding to sufficiently small neighbourhoods of points of type π+ or type π- are Pontryagin spaces.

We give necessary and sufficient conditions under which a C-0-semigroup of bi-contractions on a Krein space is similar to a semigroup of contractions on a Hilbert space. Under these and additional conditions we obtain direct sum decompositions of the Krein space into invariant regular subspaces and we describe the behavior of the semigroup on each of these summands. In the last section we give sufficient conditions for the co-generator of the semigroup to be power bounded. (C) 2004 Elsevier Inc. All rights reserved.

Certain meromorphic matrix valued functions on C\R; the so-called boundary coefficients, are characterized in terms of a standard symmetric operator S in a Pontryagin space with finite (not necessarily equal) defect numbers, a meromorphic mapping into the defect subspaces of S; and a boundary mapping for S: Under some simple assumptions the boundary coefficients also satisfy a minimality condition. It is shown that these assumptions hold if and only if for S a generalized von Neumann equality is valid. r 2002 Elsevier Science (USA). All rights reserved. MSC: primary 47B50; 47B25; 34B07; 47B32; secondary 46C20; 47A06

In the lifting theorem of B. Sz.-Nagy, C. Foias, and D. Sarason the intertwining operator A, the operator that is lifted, is a contraction from one Hilbert space to another. J. A. Ball and J. W. Helton showed that a kind of lifting theorem still holds if the negative spectral subspace of the operator I-A*A is finite dimensional. In this paper we prove that this result remains valid if the Hilbert spaces are replaced by spaces with an indefinite metric. (C) 1997 Academic Press.