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.
|Number of pages||36|
|Journal||Complex Analysis and Operator Theory|
|Publication status||Published - Mar 2008|
- self-adjoint operator function
- numerical range
- Virozub–Matsaev condition