We consider the operator A=U +K, where U is a unitary operator and K is a compact one. An eigenvalue λ of A is said to be a non-unitary one, if |λ| ≠1. We derive inequalities for sums of absolute values of the non-unitary eigenvalues. Applications of these inequalities to operator functions, spectrum perturbations and operator equations are also discussed.
- Hilbert space
- Inequalities Schatten - von Neumann operators
- Operator functions
- Spectrum perturbations
- Sylvester operator equations