Approximately finite-dimensional C*-algebras

Karl Heinrich Hofmann ; Francisco Javier Thayer

GDML_Books, (1980), p.

Résumé

CONTENTSIntroduction........................................................................................................................... 51. Finite-dimensional C*-algebras.................................................................................. 8 The objects...................................................................................................................... 8 The morphisms.............................................................................................................. 9 The matrix calculus........................................................................................................ 13 The graphic representation.......................................................................................... 16 Matrix units....................................................................................................................... 172. Almost finite-dimensional C*-algebras..................................................................... 18 The definitions................................................................................................................. 18 Examples......................................................................................................................... 22 Bratteli's scheme............................................................................................................ 23 The separable case....................................................................................................... 25 More examples................................................................................................................ 263. Ideals in AFC*-algebras................................................................................................ 284. Bratteli diagrams and partially ordered sets............................................................. 30 Augmented posets......................................................................................................... 30 Ideals of augmented posets........................................................................................ 32 The lattice of ideals of an augmented poset............................................................. 33 AFO-aJgebras and augmented posets have equivalent ideal theories............... 345. The spectral theory of augmented posets................................................................. 35 Filters and prime ideals................................................................................................ 35 Hull-kernel topologies................................................................................................... 37 AFC*-algebras and augmented posets have equivalent spectral theories........... 40 Prim A characterized for separable AFC*-algebraB................................................. 45 On the center of AFC*-algebras................................................................................... 46 The isomorphy of separable AFC*-algebras reflected in their augmented posets... 486. Problems.......................................................................................................................... 53Appendix. Some remarks on the distributivity of semilattices.................................... 54References........................................................................................................................... 58

Détail

Zbl 0451.46039

EUDML-ID : urn:eudml:doc:268488