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Integral Equations and Operator Theory

, Volume 48, Issue 4, pp 461–477 | Cite as

Bounds for Analytical Functions of Matrices

  • Michel CrouzeixEmail author
Original paper

Abstract.

If f is an analytic function bounded on a convex domain of the complex plane and A a square matrix whose spectrum is included in this domain, the function f(A) is well defined. In this paper we study bounds for ||f(A)|| uniform with respect to the functions f bounded by 1, and uniform with respect to the matrices A whose the numerical ranges are included in the domain. We show that these bounds are attained and give explicit formulae in some 2-dimensional cases.

Mathematics Subject Classification (2000).

47A12 

Keywords.

Numerical range 

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Copyright information

© Birkhäuser-Verlag 2004

Authors and Affiliations

  1. 1.Institut de Recherche Mathématique de Rennes, UMR 6625Université de Rennes 1Rennes CedexFrance

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