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

  • Operator theory
  • Banach Algebras
  • Gelfand transform

• Graduation date

  Fall 2013

• 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.