International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 7, Pages 427-428
doi:10.1155/S0161171202007962
The Cayley transform of Banach algebras
Zhidong Pan
Department of Mathematics, Saginaw Valley State University, University Center 48710, MI, USA
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.