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On a Generalization of the Gelfand Transform to Non-Commutative Banach Algebras
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- Author / Creator
- Guzman, Ivan E
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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
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- Graduation date
- Fall 2013
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- Type of Item
- Thesis
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- Degree
- Master of Science
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- 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.