Strongly 1-bounded von Neumann algebras
| dc.creator | Jung, Kenley | |
| dc.date | 2005-10-26 | |
| dc.date | 2005-10-31 | |
| dc.date.accessioned | 2026-07-07T06:47:57Z | |
| dc.date.available | 2026-07-07T06:47:57Z | |
| dc.description | Suppose F is a finite set of selfadjoint elements in a tracial von Neumann algebra M. For $α>0$, F is $α$-bounded if the free packing $α$-entropy of F is bounded from above. We say that M is strongly 1-bounded if M has a 1-bounded finite set of selfadjoint generators F such that there exists an x in F with finite free entropy. It is shown that if M is strongly 1-bounded, then any finite set of selfadjoint generators G for M is 1-bounded and the microstates free entropy dimension of G is less than or equal to 1; consequently, a strongly 1-bounded von Neumann algebra is not isomorphic to an interpolated free group factor and the microstates free entropy dimension is an invariant for these algebras. Examples of strongly 1-bounded von Neumann algebras include (separable) II_1-factors which have property Gamma, have Cartan subalgebras, are non-prime, or the group von Neumann algebras of SL_n(Z), n >2. If M and N are strongly 1-bounded and their intersection is diffuse, then the von Neumann algebra generated by M and N is strongly 1-bounded. In particular, a free product of two strongly 1-bounded von Neumann algebras with amalgamation over a common, diffuse von Neumann subalgebra is strongly 1-bounded. It is also shown that a II_1-factor generated by the normalizer of a strongly 1-bounded von Neumann subalgebra is strongly 1-bounded. | |
| dc.description | 15 pages, added references, minor corrections | |
| dc.identifier | https://arxiv.org/abs/math/0510576 | |
| dc.identifier | http://arxiv.org/abs/math/0510576 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103827 | |
| dc.subject | Operator Algebras | |
| dc.subject | Primary 46L54; Secondary 28A75 | |
| dc.title | Strongly 1-bounded von Neumann algebras | |
| dc.type | text |