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The Virozub–Matsaev Condition and Spectrum of Definite Type for Self-adjoint Operator Functions |
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| Authors: | Heinz Langer Matthias Langer Alexander Markus Christiane Tretter |
| Institution: | 1. Institut für Analysis und Scientific Computing, Technische Universit?t Wien, Wiedner Hauptstr. 8–10, A-1040, Wien, Austria 2. Department of Mathematics, University of Strathclyde, 26 Richmond Street, Glasgow, G1 1XH, United Kingdom 3. Department of Mathematics, Ben-Gurion University of the Negev, IL-84105, Beer Sheva, Israel 4. Mathematisches Institut, Universit?t Bern, Sidlerstr. 5, CH-3012, Bern, Switzerland |
| 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. Received: September 22, 2007. Accepted: September 29, 2007. |
| Keywords: | Primary 47A56 Secondary 47A10 47A12 47B50 |
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