Resolvents of operators on tensor products of Euclidean spaces. Issue 4 (2nd April 2016)

• Record Type: Journal Article
• Authors: Gil', Michael
• Is Part Of: Linear & multilinear algebra. Volume 64:Issue 4(2016)
• Page Start: 699
• Page End: 716
• Publication Date: 2016-04-02
• Subjects: matrices -- Kronecker product -- resolvent -- matrix equation -- invariant subspace -- differential equation; 15A69 -- 15A18 -- 15A24 -- 15A45; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2015.1083934
• Languages: English
• ISSNs: 0308-1087

Abstract

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.