Nagy-Foias type functional models of nondissipative operators in parabolic domains

Details Nagy-Foias type functional models of nondissipative operators in parabolic domains Nagy-Foias type functional models of nondissipative operators in parabolic domains

2006-07-03

arxiv.org/abs/math/0607062v2

J. Operator Theory 60 (2008), no. 1, 3-28

Mathematics

Functional Analysis

31 pages

Scientific paper

A functional model for nondissipative unbounded perturbations of an unbounded self-adjoint operator on a Hilbert space X is constructed. This model is analogous to the Nagy--Foias model of dissipative operators, but it is linearly similar and not unitarily equivalent to the operator. It is attached to a domain of parabolic type, instead of a half-plane. The transformation map from X to the model space and the analogue of the characteristic function are given explicitly. All usual consequences of the Nagy--Foias construction (the H-infty calculus, the commutant lifting, etc.) hold true in our context.

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