Some Exact Sequences for Toeplitz Algebras of Spherical Isometries
| dc.creator | Prunaru, Bebe | |
| dc.date | 2005-11-14 | |
| dc.date.accessioned | 2026-07-07T06:51:12Z | |
| dc.date.available | 2026-07-07T06:51:12Z | |
| dc.description | A family $\{T_j\}_{j\in J}$ of commuting Hilbert space operators is said to be a spherical isometry if $\sum_{j\in J}T^*_jT_j=1$ in the weak operator topology. We show that every commuting family $\Cal F$ of spherical isometries has a commuting normal extension $\hat{\Cal F}$. Moreover, if $\hat{\Cal F}$ is minimal, then there exists a natural short exact sequence $0\to\Cal C\to C^*(\Cal F)\to C^*(\hat{\Cal F})\to 0$ with a completely isometric cross-section, where $\Cal C$ is the commutator ideal in $C^*(\Cal F)$. We also show that the space of Toeplitz operators associated to $\Cal F$ is completely isometric to the commutant of the minimal normal extension $\hat{\Cal F}$. Applications of these results are given for Toeplitz operators on strictly pseudoconvex or bounded symmetric domains. | |
| dc.identifier | https://arxiv.org/abs/math/0511340 | |
| dc.identifier | http://arxiv.org/abs/math/0511340 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/104910 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | Primary 47L80; 47B35; Secondary 47B20; 46L07 | |
| dc.title | Some Exact Sequences for Toeplitz Algebras of Spherical Isometries | |
| dc.type | text |