Continuity versus boundedness of the spectral factorization mapping

Holger Boche ¹   ; Volker Pohl ²

¹ Heinrich-Hertz Chair for Mobile Communications Department of EECS Technische Universität Berlin Einsteinufer 25 10587 Berlin, Germany
² Department of Electrical Engineering Technion – Israel Institute of Technology Haifa 32000, Israel

Studia Mathematica, Tome 189 (2008) no. 2, pp. 131-145

Résumé

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.

Détail

DOI : 10.4064/sm189-2-4

Keywords: paper characterizes banach algebras continuous functions which spectral factorization mapping mathfrak continuous bounded shown mathfrak continuous only riesz projection bounded algebra mathfrak bounded only algebra isomorphic algebra continuous functions consequently mathfrak never continuous bounded algebra under consideration