Continuity versus boundedness of the spectral factorization mapping

• Autorzy: Holger Boche , Volker Pohl
• Języki publikacji: EN

Abstrakty

EN

This paper characterizes the Banach algebras of continuous functions on which the spectral factorization mapping 𝔖 is continuous or bounded. It is shown that 𝔖 is continuous if and only if the Riesz projection is bounded on the algebra, and that 𝔖 is bounded only if the algebra is isomorphic to the algebra of continuous functions. Consequently, 𝔖 can never be both continuous and bounded, on any algebra under consideration.

Kategorie tematyczne

• 46J10: Banach algebras of continuous functions, function algebras
• 47A68: Factorization theory (including Wiener-Hopf and spectral factorizations)
• 47H99: None of the above, but in this section
• 46J15: Banach algebras of differentiable or analytic functions, H p -spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 189
• Numer: 2
• Strony: 131-145

Daty

wydano

2008

Twórcy

autor

Holger Boche

• Heinrich-Hertz Chair for Mobile Communications, Department of EECS, Technische Universität Berlin, Einsteinufer 25, 10587 Berlin, Germany

autor

Volker Pohl

• Department of Electrical Engineering, Technion - Israel Institute of Technology, Haifa 32000, Israel

Identyfikatory

DOI

10.4064/sm189-2-4