Resolvents of operators on tensor products of Euclidean spaces. Issue 4 (2nd April 2016) - Gil', Michael
Abstract : We consider the operator where 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 equation and 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.