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The Virozub-Matsaev condition and spectrum of definite type for self-adjoint operator functions

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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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
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: 23 Jul 2015 11:31
URI: http://strathprints.strath.ac.uk/id/eprint/13640

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