The Cayley transform of Banach algebras
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.
scientific article; zbMATH DE number 1780360