School of Mathematics
School of Mathematics
Module MA442C - Banach algebras
2009-10 (SS Mathematics, SS Two-Subject Moderatorship
)
Lecturer: Dr. Rupert Levene
Requirements/prerequisites:
prerequisite: 321
Duration: Michaelmas term, 11 weeks
Number of lectures per week: 3 lectures including tutorials per week
Assessment:
End-of-year Examination:
2 hour examination in Trinity term.
Description:
- Introduction to Banach algebras
- Definition and examples
- invertibility
- the spectrum
- quotients of Banach algebras
- ideals, quotients and homomorphisms.
- Weak topologies
- Subbases and weak topologies
- The product topology and Tychonoff's theorem.
- The weak* topology and the Banach-Alaoglu theorem.
- Unital abelian Banach algebras
- Characters and maximal ideals
- The Gelfand representation.
- C*-algebras
- Definitions and examples
- The Stone-Weierstrass theorem
- Abelian C*-algebras and the continuous functional calculus.
- Positive elements of C*-algebras
- the GNS representation.
The treatment will be based in part on some of the book: Gerard J. Murphy,
C*-Algebras and Operator Theory,
Academic Press,
(1990).
Mar 4, 2010
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On 4 Mar 2010, 10:51.