Continuity versus boundedness of the spectral factorization mapping

Tom 189 / 2008

Holger Boche, Volker Pohl Studia Mathematica 189 (2008), 131-145 MSC: Primary 47A68, 47H99, 46J10; Secondary 46J15. DOI: 10.4064/sm189-2-4

Streszczenie

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.

Autorzy

  • Holger BocheHeinrich-Hertz Chair for Mobile Communications
    Department of EECS
    Technische Universität Berlin
    Einsteinufer 25
    10587 Berlin, Germany
    e-mail
  • Volker PohlDepartment of Electrical Engineering
    Technion – Israel Institute of Technology
    Haifa 32000, Israel
    e-mail

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