Continuity versus boundedness of the spectral factorization mapping
Volume 189 / 2008
Studia Mathematica 189 (2008), 131-145
MSC: Primary 47A68, 47H99, 46J10; Secondary 46J15.
DOI: 10.4064/sm189-2-4
Abstract
This paper characterizes the Banach algebras of continuous functions on which the spectral factorization mapping $\mathfrak{S}$ is continuous or bounded. It is shown that $\mathfrak{S}$ is continuous if and only if the Riesz projection is bounded on the algebra, and that $\mathfrak{S}$ is bounded only if the algebra is isomorphic to the algebra of continuous functions. Consequently, $\mathfrak{S}$ can never be both continuous and bounded, on any algebra under consideration.
