A bound for norms of functions of matrices

AbstractIf A is an m×m and ⨍ is an analytic function, then ⨍(A) depends only on the values of ⨍ and its first m−1 derivatives on the spectrum of A. In this paper we estimate ‖⨍(A)‖, for certain matrix norms ‖·‖, in terms of the maximum moduli of these derivatives on the convex hull of the spectrum of A