Spatial discretization of Cuntz algebras
| dc.creator | Roch, Steffen | |
| dc.date | 2008-11-19 | |
| dc.date.accessioned | 2026-07-07T10:19:28Z | |
| dc.date.available | 2026-07-07T10:19:28Z | |
| dc.description | The (abstract) Cuntz algebra is generated by non-unitary isometries and has therefore no intrinsic finiteness properties. To approximate the elements of the Cuntz algebra by finite-dimensional objects, we thus consider a spatial discretization of this algebra by the finite sections method. For we represent the Cuntz algebra as a (concrete) algebra of operators on a Hilbert space and associate with each operator in this algebra the sequence of its finite sections. The goal of this paper is to examine the structure of the $C^*$-algebra which is generated by all sequences of this form. Our main results are the fractality of a suitable restriction of this sequence algebra and a necessary and sufficient criterion for the stability of sequences in the restricted algebra. These results are employed to study spectral and pseudospectral approximations of elements of the Cuntz algebra. | |
| dc.description | 48 pages | |
| dc.identifier | https://arxiv.org/abs/0811.3072 | |
| dc.identifier | http://arxiv.org/abs/0811.3072 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174519 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L99; 47N40; 47L80; 65J10 | |
| dc.title | Spatial discretization of Cuntz algebras | |
| dc.type | text |