On a Class of Ideals of the Toeplitz Algebra on the Bergman Space of the Unit Ball
| dc.creator | Le, Trieu | |
| dc.date | 2007-05-07 | |
| dc.date.accessioned | 2026-07-07T07:59:50Z | |
| dc.date.available | 2026-07-07T07:59:50Z | |
| dc.description | Let $\mathfrak{T}$ denote the full Toeplitz algebra on the Bergman space of the unit ball $\mathbb{B}_n.$ For each subset $G$ of $L^{\infty},$ let $\mathfrak{CI}(G)$ denote the closed two-sided ideal of $\mathfrak{T}$ generated by all $T_fT_g-T_gT_f$ with $f,g\in G.$ It is known that $\mathfrak{CI}(C(\bar{\mathbb{B}}_n))=\mathcal{K}$ - the ideal of compact operators and $\mathfrak{CI}(C(\mathbb{B}_n))=\mathfrak{T}.$ Despite these ``extremal cases'', $\mathfrak{T}$ does contain other non-trivial ideals. This paper gives a construction of a class of subsets $G$ of $L^{\infty}$ so that $\mathcal{K}\subsetneq\mathfrak{CI}(G)\subsetneq\mathfrak{T}.$ | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/0705.0970 | |
| dc.identifier | http://arxiv.org/abs/0705.0970 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/128520 | |
| dc.subject | Functional Analysis | |
| dc.subject | 47B35 | |
| dc.title | On a Class of Ideals of the Toeplitz Algebra on the Bergman Space of the Unit Ball | |
| dc.type | text |