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On a Generalization of the Gelfand Transform to Non-Commutative Banach Algebras

  • Author / Creator
    Guzman, Ivan E
  • A Gelfand theory for an arbitrary Banach algebra A is a pair (G;A), such that: A is a C*-algebra and G : A ! A is an algebra homomorphism; G induces a bijection between the set of maximal modular left ideals of A and the set of maximal modular left ideals of A; and for every maximal modular left ideal L of A, the map GL : A=G1(L) ! A=L induced by G has dense range. We prove that if A is a postliminal C*-algebra with Gelfand theory (G;A), then no proper C*-subalgebra of A contains GA. We also show that if J is an ideal of a Banach algebra A such that A=J and J both have Gelfand theories, then A also has a Gelfand theory if we impose some conditions on J and on its Gelfand theory.

  • Subjects / Keywords
  • Graduation date
    2013-11
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/R3FB4WV4R
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Master's
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Mathematics
  • Supervisor / co-supervisor and their department(s)
    • Runde, Volker (Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Lau, Anthony (Mathematical and Statistical Sciences)
    • Runde, Volker (Mathematical and Statistical Sciences)
    • Yaskin, Vladyslav (Mathematical and Statistical Sciences)
    • Bowman, John (Mathematical and Statistical Sciences)
    • Berger, Arno (Mathematical and Statistical Sciences)