COMMUTATOR IDEALS OF SUBALGEBRAS OF TOEPLITZALGEBRAS ON WEIGHTED BERGMAN SPACES

摘要

For a > --1, let A_α~2 denote the corresponding weighted Bergmanspace of the unit ball. For any self-adjoint subset G ∈ L~∞, let T(G) denote theC*-subalgebra of (A_α~2) generated by {T_f : f ∈ G} . Let eI(G) denote thecommutator ideal of T(G). It was showed by D. Suarez (in 2004 for n = 1) and by the author (in 2006 for all n ≥1) that ET(L~∞) = T(L~∞) in the case a = 0. In this paper we show that in the setting of weighted Bergman spaces, the identity ET(G) = T(G) holds true for a class of subsets G including L~V.