Abstract
Let H be a Krein space and U a unitary operator in H. Assume that for a certain open subset ¦£ of the unit circle T no point of Γ is accumulation point of the nonunitary spectrum σ(U)\T of U and that every point of Γ can be connected with 0 and ∞ by curves in the resolvent set ρ(U). Such an operator is called definitizable over Γ, if, roughly speaking, it has a spectral function over ¦£ (in the sense of the theory of definitizable operators). This class of operators, of course, contains the definitizable unitary operators in H. The main concern of this paper is to study some aspects of the behaviour of the spectral functions under compact perturbations of the corresponding operators within this class.
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© 1986 Springer Basel AG
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Jonas, P. (1986). On a Class of Unitary Operators in Krein Space. In: Douglas, R.G., Pearcy, C.M., Sz.-Nagy, B., Vasilescu, FH., Voiculescu, D., Arsene, G. (eds) Advances in Invariant Subspaces and Other Results of Operator Theory. Operator Theory: Advances and Applications, vol 17. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7698-8_12
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DOI: https://doi.org/10.1007/978-3-0348-7698-8_12
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