H. Langer, M. Langer, A. Markus and C. Tretter,
The Virozub–Matsaev condition and spectrum of definite type for
self-adjoint operator functions,
Complex Anal. Oper. Theory 2 (2008), 99–134
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.