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A canonical form for self-adjoint pencils in Hilbert space

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Abstract

We characterize those pencils P=λA−B of operators on a separable Hilbert space H for which a linear homeomorphism D of H exists satisfying the following: (i) H decomposes into a direct sum F+G, orthogonal in a (perhaps indefinite) inner product induced by A, where F is finite dimensional (ii) D*PD=PF⊕(λIG−C) where PF is a (congruence) canonical form for the general self-adjoint pencil on F, and C is a bounded self-adjoint operator on G. For a given P, explicit constructions are given for C, D, F, G and PF.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Calgary, T2N 1N4, Calgary, Alberta, Canada

    Paul Binding

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  1. Paul Binding
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Binding, P. A canonical form for self-adjoint pencils in Hilbert space. Integr equ oper theory 12, 324–342 (1989). https://doi.org/10.1007/BF01235736

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  • DOI: https://doi.org/10.1007/BF01235736

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