The Cayley transform of Banach algebras

Abstract

The main result of Haynes (1991) is that a square matrix is convergent (limn→∞Dn=0) if and only if it is the Cayley transform CA=(I−A)−1(I+A) of a stable matrix A. In this note, we show, with a simple proof, that the above is true in a much more general setting of complex Banach algebras.