LAUSR

Let $$\mu $$ μ be a regular Borel measure on the open unit ball B in $$\mathbf{C}^n$$ C n . By a natural formula, it gives rise to a Toeplitz operator $$T_\mu $$ T μ on the Hardy space $$H^2(S)$$ H 2 ( S ) . We characterize the membership of $$T_\mu ^s$$ T μ s , $$0 < s \le 1$$ 0 < s ≤ 1 , in any norm ideal $${\mathcal {C}}_\Phi $$ C Φ that satisfies condition (DQK). The same techniques allow us to compute the Dixmier trace of $$T_\mu $$ T μ when $$T_\mu \in {\mathcal {C}}_1^+$$ T μ ∈ C 1 + .