Ideal Structure in Free Semigroupoid Algebras from Directed Graphs
| dc.creator | Jury, Michael T. | |
| dc.creator | Kribs, David W. | |
| dc.date | 2003-09-24 | |
| dc.date.accessioned | 2026-07-07T06:42:22Z | |
| dc.date.available | 2026-07-07T06:42:22Z | |
| dc.description | A free semigroupoid algebra is the weak operator topology closed algebra generated by the left regular representation of a directed graph. We establish lattice isomorphisms between ideals and invariant subspaces, and this leads to a complete description of the weak operator topology closed ideal structure for these algebras. We prove a distance formula to ideals, and this gives an appropriate version of the Caratheodory interpolation theorem. Our analysis rests on an investigation of predual properties, specifically the $A_n$ properties for linear functionals, together with a general Wold Decomposition for $n$-tuples of partial isometries. A number of our proofs unify proofs for subclasses appearing in the literature. | |
| dc.description | 32 pages, J. Operator Theory, to appear | |
| dc.identifier | https://arxiv.org/abs/math/0309397 | |
| dc.identifier | http://arxiv.org/abs/math/0309397 | |
| dc.identifier | J. Operator Theory, 53 (2005), 273-302. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/102018 | |
| dc.subject | Operator Algebras | |
| dc.subject | 47L55, 47L75 | |
| dc.title | Ideal Structure in Free Semigroupoid Algebras from Directed Graphs | |
| dc.type | text |