Langer, M. and Langer, Heinz and Markus, Alexander and Tretter, Christiane
(2008)
*The Virozub-Matsaev condition and spectrum of definite type for self-adjoint operator functions.*
Complex Analysis and Operator Theory, 2 (1).
pp. 99-134.
ISSN 1661-8254

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Official URL: http://dx.doi.org/10.1007/s11785-007-0032-z

## Abstract

We establish sufficient conditions for the so-called Virozub-Matsaev condition for twice continuously differentiable self-adjoint operator functions. This condition is closely related to the existence of a local spectral function and to the notion of positive type spectrum. Applications to self-adjoint operators in Krein spaces and to quadratic operator polynomials are given.

Item type: | Article |
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ID code: | 13640 |

Keywords: | self-adjoint operator function, numerical range, spectrum, Virozub–Matsaev condition, Probabilities. Mathematical statistics, Mathematics, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics |

Subjects: | Science > Mathematics > Probabilities. Mathematical statistics Science > Mathematics |

Department: | Faculty of Science > Mathematics and Statistics |

Depositing user: | Mrs Carolynne Westwood |

Date Deposited: | 06 Jan 2010 16:44 |

Last modified: | 11 Dec 2015 23:02 |

URI: | http://strathprints.strath.ac.uk/id/eprint/13640 |

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