Convexity properties of distinguished eigenvalues of certain classes of operators
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- by B. Najman PDF
- Proc. Amer. Math. Soc. 111 (1991), 221-225 Request permission
Abstract:
We prove two convexity results: (1) Let $A(\varepsilon ) = {A_0} + \varepsilon {A_1}$ be a family of selfadjoint operators in a Krein space with separated spectrum so that the maximum $\lambda \_(\varepsilon )$ of the spectrum of negative type of $A(\varepsilon )$ is an isolated simple eigenvalue. Then $\lambda \_(\varepsilon )$ is convex. (2) Let $\lambda \_(\varepsilon )$ be the left distinguished eigenvalue of the generalized eigenvalue problem $({A_0} + \varepsilon {A_1})x = \lambda Bx$ where ${A_1}$ and $B$ are real diagonal matrices and ${A_0}$ is an irreducible essentially nonnegative matrix. Then $\lambda \_(\varepsilon )$ is convex. In both cases $\lambda \_(\varepsilon )$ is strictly convex unless it is linear.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 111 (1991), 221-225
- MSC: Primary 47A55; Secondary 15A18, 47A70, 47B15, 47B50
- DOI: https://doi.org/10.1090/S0002-9939-1991-1027100-4
- MathSciNet review: 1027100