A Remark on Commutativity of the Image of A-Valued Analytic Function

摘要

Let BL(H) be a complex Banach algebra of all bounded linear operators acting on the Hilbert space H. J. Globevnik and I. Vidav proved that when the range of an operator-valued analytic function with domain of definition V is containd in C consists of the normal operators, then f(D) is a commutative set in the algebra BL(H). The paper strengthens this result for the topological algebras.