Endomorphisms of B(H), extensions of pure states, and a class of representations of O_n
| dc.creator | Fowler, Neal | |
| dc.creator | Laca, Marcelo | |
| dc.date | 1997-09-26 | |
| dc.date.accessioned | 2026-07-07T09:13:51Z | |
| dc.date.available | 2026-07-07T09:13:51Z | |
| dc.description | Let F_n be the fixed-point algebra of the gauge action of the circle on the Cuntz algebra O_n. For every pure state ρof F_n and every representation θof C(T) we construct a representation of O_n, and we use the resulting class of representations to parameterize the space of all states of O_n which extend ρ. We show that the gauge group acts transitively on the pure extensions of ρand that the action is p-to-1 with p the period of ρunder the usual shift. We then use the above representations of O_n to construct endomorphisms of B(H) which we classify up to conjugacy in terms of the parameters ρand θ. In particular our construction yields every ergodic endomorphism αwhose tail algebra $\bigcap_kα^k(B(H))$ has a minimal projection, and our results classify these ergodic endomorphisms by an equivalence relation on the pure states of F_n. As examples we analyze the ergodic endomorphisms arising from periodic pure product states of F_n, for which we are able to give a geometric complete conjugacy invariant, generalizing results of Stacey, Laca, and Bratteli-Jorgensen-Price on the shifts of Powers. | |
| dc.description | 22 pages, AMS-LaTeX | |
| dc.identifier | https://arxiv.org/abs/funct-an/9709004 | |
| dc.identifier | http://arxiv.org/abs/funct-an/9709004 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152467 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.title | Endomorphisms of B(H), extensions of pure states, and a class of representations of O_n | |
| dc.type | text |