The Cayley transform of Banach algebras
type: Item
instance of: scholarly article
title: The Cayley transform of Banach algebras
zbMATH Open document ID: 0999.15002
DOI: 10.1155/S0161171202007962
author: Zhidong Pan
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2002-08-13T00:00:00Z
full work available at URL: https://eudml.org/doc/49551
full work available at URL: S0161171202007962.html
review text: Summary: The main result of \textit{T. Haynes} [ibid. 14, No. 1, 77-82 (1991; Zbl 0718.15003)] is that a square matrix is convergent (\(\lim_{n \rightarrow \infty} D^n = 0\)) if and only if it is the Cayley transform \(C_A = (I-A)^{-1}(I+A)\) 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.
Mathematics Subject Classification ID: 15A04
Mathematics Subject Classification ID: 47A60
Mathematics Subject Classification ID: 47C05
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 1780360
zbMATH Keywords: convergent matrix
zbMATH Keywords: stable matrix
zbMATH Keywords: Cayley transform
zbMATH Keywords: complex Banach algebras
MaRDI profile type: Publication
OpenAlex ID: W2072304994
description: scientific article; zbMATH DE number 1780360