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International Journal of Mathematics and Mathematical Sciences
Volume 29, Issue 7, Pages 427-428

The Cayley transform of Banach algebras

Department of Mathematics, Saginaw Valley State University, University Center 48710, MI, USA

Received 30 July 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The main result of Haynes (1991) is that a square matrix is convergent (limnDn=0) if and only if it is the Cayley transform CA=(IA)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.