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.
- Numerical range
- Self-adjoint operator function
ASJC Scopus subject areas
- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics