Symbolic calculus on a Banach algebra of continuous functions (Q1316370)

The author studies the symbolic calculus on Banach algebras of continuous functions and related spaces. In particular, functions operating on the real part of the algebra are considered. The main tool in this paper is an ultraseparation argument. As a consequence he shows for example, that \(t^ p\) on \([0,1)\) for any \(p\) with \(0<p<1\) does not operate on the real part of a Banach function algebra on a compact Hausdorff space unless the algebra contains every continuous function.