Values of the Pukanszky Invariant in McDuff Factors
| dc.creator | White, Stuart | |
| dc.date | 2006-09-10 | |
| dc.date | 2007-11-02 | |
| dc.date.accessioned | 2026-07-07T09:30:53Z | |
| dc.date.available | 2026-07-07T09:30:53Z | |
| dc.description | In 1960 Pukánszky introduced an invariant associating to every masa in a separable $\mathrm{II}_1$ factor a non-empty subset of $\mathbb N\cup\{\infty\}$. This invariant examines the multiplicity structure of the von Neumann algebra generated by the left-right action of the masa. In this paper it is shown that every non-empty subset of $\mathbb N\cup\{\infty\}$ arises as the Pukánszky invariant of some masa in a separable McDuff $\mathrm{II}_1$ factor which contains a masa with Pukánszky invariant $\{1\}$. In particular the hyperfinite $\mathrm{II}_1$ factor and all separable McDuff $\mathrm{II}_1$ factors with a Cartan masa satisfy this hypothesis. In a general separable McDuff factor we show that every subset of $\mathbb N\cup\{\infty\}$ containing $\infty$ is obtained as a Pukánskzy invariant of some masa. | |
| dc.description | 26 pages, minor typos corrected | |
| dc.identifier | https://arxiv.org/abs/math/0609269 | |
| dc.identifier | http://arxiv.org/abs/math/0609269 | |
| dc.identifier | J. Funct. Anal. 254 (2008), no. 3, 612--631. | |
| dc.identifier | doi:10.1016/j.jfa.2007.10.011 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158268 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L10 | |
| dc.title | Values of the Pukanszky Invariant in McDuff Factors | |
| dc.type | text |