discipline 
Pure Mathematics 
subject 
Banach
algebras 
lecturers 
János Kristóf 
credits 
2 
period 

curriculum 
Character space of an algebra, general Gelfand
representation, polynomial functional calculus, normed
algebras, theorem of GelfandMazur, entire function
calculus, Gelfand representation of a Banach
algebra, I, II and III type of *algebras, Banach *algebras and C*algebras,
first theorem of GelfandNaimark, continuous
functional calculus, the covering C*algebra of a Banach *algebra, abstract
Stone theorem, positivity in C*algebras, existence of approximate unties, monotone sequentially closed
C*algebras, polar decomposition in MSCalgebras 
literature 
N. Bourbaki: Théories
spectrales J. Dixmier: Les C*algébres
et leurs representations 
form of tuition 
Lectures 
mode of assessment 
oral exam 