Fractal entropies and dimensions for microstate spaces
| dc.creator | Jung, Kenley | |
| dc.date | 2002-12-01 | |
| dc.date | 2003-09-10 | |
| dc.date.accessioned | 2026-07-07T04:53:26Z | |
| dc.date.available | 2026-07-07T04:53:26Z | |
| dc.description | Using Voiculescu's notion of a matricial microstate we introduce fractal dimensions and entropies for finite sets of selfadjoint operators in a tracial von Neumann algebra. We show that they possess properties similar to their classical predecessors. We relate the new quantities to free entropy and free entropy dimension and show that a modified version of free Hausdorff dimension is an algebraic invariant. We compute the free Hausdorff dimension in the cases where the set generates a finite dimensional algebra or where the set consists of a single selfadjoint. We show that the free Hausdorff dimension becomes additive for such sets in the presence of freeness. | |
| dc.description | 25 pages, minor corrections, lifting of restrictive conditions for the computation of dimension of a single selfadjoint, additional lemma in section 6 | |
| dc.identifier | https://arxiv.org/abs/math/0212013 | |
| dc.identifier | http://arxiv.org/abs/math/0212013 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65851 | |
| dc.subject | Operator Algebras | |
| dc.subject | Metric Geometry | |
| dc.subject | Primary 46L54; Secondary 28A78 | |
| dc.title | Fractal entropies and dimensions for microstate spaces | |
| dc.type | text |