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Extended Functional Calculus

  • Béla Sz.-Nagy
  • Hari BercoviciEmail author
  • Ciprian Foias
  • László Kérchy
Chapter
  • 1.9k Downloads
Part of the Universitext book series (UTX)

Abstract

We extend our functional calculus for a contraction T on \(\mathfrak{K}\) so that certain unbounded functions are also allowed. Let us recall the definitions of the classes \(H^\infty_T\) and \(K^\infty_T\) as given in Secs. 2 and 3 of the preceding chapter: \(H^\infty_T\) consists of the functions \(u\in H^\infty\) ??for which the strong operator limit \(u(T)=lim_{r\rightarrow1-0} u_r(T)\) exists, and \(K^\infty_T\) consists of those functions \(u\in H^\infty_T \) for which \(u(T)^{-1}\) exists and \(K^\infty_T\) is densely defined in \(\mathfrak{H}\). The class \(H^\infty_T\) is an algebra, and the class \(K^\infty_T\) is multiplicative.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Béla Sz.-Nagy
  • Hari Bercovici
    • 1
    Email author
  • Ciprian Foias
    • 2
  • László Kérchy
    • 3
  1. 1.Mathematics DepartmentIndiana UniversityBloomingtonUSA
  2. 2.Mathematics DepartmentTexas A & M UniversityCollege StationUSA
  3. 3.Bolyai InstituteSzeged UniversitySzegedHungary

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