On dense ideals of $C^\ast $-algebras and generalizations of the Gelfand–Naimark Theorem

Tom 215 / 2013

Jorma Arhippainen, Jukka Kauppi Studia Mathematica 215 (2013), 71-98 MSC: 46J10, 46J25, 46J30. DOI: 10.4064/sm215-1-5

Streszczenie

We develop the theory of Segal algebras of commutative $C^\ast $-algebras, with an emphasis on the functional representation. Our main results extend the Gelfand–Naimark Theorem. As an application, we describe faithful principal ideals of $C^\ast $-algebras. A key ingredient in our approach is the use of Nachbin algebras to generalize the Gelfand representation theory.

Autorzy

  • Jorma ArhippainenDepartment of Mathematical Sciences
    University of Oulu
    P.O. Box 3000
    SF 90014 Oulun yliopisto, Finland
    e-mail
  • Jukka KauppiDepartment of Mathematical Sciences
    University of Oulu
    P.O. Box 3000
    SF 90014 Oulun yliopisto, Finland
    e-mail

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