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.
- self-adjoint operator function
- numerical range
- Virozub–Matsaev condition
Langer, M., Langer, H., Markus, A., & Tretter, C. (2008). The Virozub-Matsaev condition and spectrum of definite type for self-adjoint operator functions. Complex Analysis and Operator Theory, 2(1), 99-134. https://doi.org/10.1007/s11785-007-0032-z