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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A class of maps in an algebra with indefinite metric


Author: Angelo B. Mingarelli
Journal: Proc. Amer. Math. Soc. 121 (1994), 1177-1183
MSC: Primary 47B50; Secondary 34A12, 46C20, 46H99, 47N20
MathSciNet review: 1197541
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Abstract: We study a class of hermitian maps on an algebra endowed with an indefinite inner product. We show that, in particular, the existence of a non-real eigenvalue is incompatible with the existence of a real eigenvalue having a right-invertible eigenvector. It also follows that for this class of maps the existence of an appropriate extremal for an indefinite Rayleigh quotient implies the nonexistence of nonreal eigenvalues. These results are intended to complement the Perron-Fröbenius and Kreĭn-Rutman theorems, and we conclude the paper by describing applications to ordinary and partial differential equations and to tridiagonal matrices.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1197541-6
PII: S 0002-9939(1994)1197541-6
Keywords: Kreĭn space, hermitian maps, Perron-Fröbenius
Article copyright: © Copyright 1994 American Mathematical Society