Locally inner automorphisms of operator algebras
| dc.creator | Sherman, David | |
| dc.date | 2006-09-26 | |
| dc.date | 2008-02-29 | |
| dc.date.accessioned | 2026-07-07T09:23:50Z | |
| dc.date.available | 2026-07-07T09:23:50Z | |
| dc.description | In this paper an automorphism of a unital C*-algebra is said to be /locally inner/ if on any element it agrees with some inner automorphism. We make a fairly complete study of local innerness in von Neumann algebras, incorporating comparison with the pointwise innerness of Haagerup-Stormer. On some von Neumann algebras, including all with separable predual, a locally inner automorphism must be inner. But a transfinitely recursive construction demonstrates that this is not true in general. As an application, we show that the diagonal sum descends to a well-defined map on the automorphism orbits of a unital C*-algebra if and only if all its automorphisms are locally inner. | |
| dc.description | 17 pages; some substantive changes to the last section ("problems and comments") | |
| dc.identifier | https://arxiv.org/abs/math/0609735 | |
| dc.identifier | http://arxiv.org/abs/math/0609735 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155879 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L40, 47C15 | |
| dc.title | Locally inner automorphisms of operator algebras | |
| dc.type | text |