Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4603198 | Linear Algebra and its Applications | 2007 | 6 Pages |
Abstract
Let A be a finite direct sum of full matrix algebras over the complex field. We prove that if F is a holomorphic map of the open spectral unit ball of A into itself such that F(0)=0 and F′(0)=I, the identity of A, then a and F(a) have always the same spectrum. As an application we obtain a new proof, purely function-theoretic, of the fact that a unital spectral isometry on a finite-dimensional semi-simple Banach algebra is a Jordan morphism.
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