Article ID Journal Published Year Pages File Type
4603608 Linear Algebra and its Applications 2007 9 Pages PDF
Abstract

We show that an algebraic operator on a complex Banach space has reflexive commutant if and only if each zero of the minimal polynomial of the operator is simple. Further, for any operator, the local commutant at an eigenvector is reflexive. On the other hand, for an algebraic operator whose minimal polynomial has at least one zero that is not simple, the local commutant of the operator at a given vector is reflexive precisely when the vector is an eigenvector.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory