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 Gelfand-Mazur, entire function calculus, Gelfand representation of a Banach algebra, I, II and III type of *-algebras, Banach *-algebras and C*-algebras, first theorem of Gelfand-Naimark, 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 MSC-algebras

 

literature

N. Bourbaki: Théories spectrales

J. Dixmier: Les C*-algébres et leurs representations

 

form of tuition

Lectures

mode of assessment

oral exam