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On a Generalization of the Gelfand Transform to NonCommutative 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
 201311

 Type of Item
 Thesis

 Degree
 Master of Science

 License
 This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for noncommercial 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.