Resolvents of operators on tensor products of Euclidean spaces
Michael I. Gil’ · Linear and Multilinear Algebra · 2015
We consider the operatorwhere are matrices , means the tensor product. Norm estimates for the resolvent of that operator are derived. By these estimates, we obtain bounds for a solution of the equationand explore perturbations of that equation. The norm estimates for the resolvent of enable us to establish a bound for the distance between invariant subspaces of two matrices. Besides, the well-known Davis–Kahan result is particularly generalized. In addition, we derive a new stability test for non-linear non-autonomous ordinary differential equations.