%0 Journal Article
%T On a Class of Ideals of the Toeplitz Algebra on the Bergman Space of the Unit Ball
%A Trieu Le
%J Mathematics
%D 2007
%I arXiv
%X 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 $\mathcal{K}\subsetneq\mathfrak{CI}(G)\subsetneq\mathfrak{T}.$
%U http://arxiv.org/abs/0705.0970v1