A variational principle in Kreĭn space

Binding, Paul; Najman, Branko

doi:10.1090/S0002-9947-1994-1181181-3

A variational principle in Kreĭn space
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by Paul Binding and Branko Najman PDF

Trans. Amer. Math. Soc. 342 (1994), 489-499 Request permission

Abstract:

A variational characterization, involving a max-inf of the Rayleigh quotient, is established for certain eigenvalues of a wide class of definitizable selfadjoint operators Q in a Krein space. The operator Q may have continuous spectrum and nonreal and nonsemisimple eigenvalues; in particular it may have embedded eigenvalues. Various applications are given to selfadjoint linear and quadratic eigenvalue problems with weak definiteness assumptions.

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