Let ${mathcal T}$ be the $C^ast $-algebra generated by the Toeplitz operators ${T_varphi : varphi in L^infty (S,dsigma )}$ on the Hardy space $H^2(S)$ of the unit sphere in $mathbf{C}^n$. It is well known that ${mathcal T}$ is contained in the essential commutant of ${T_varphi : varphi in operatorname{VMO}cap L^infty (S,dsigma )}$. We show that the essential commutant of ${T_varphi : varphi in operatorname{VMO}cap L^infty (S,dsigma )}$ is strictly larger than ${mathcal T}$.
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机译：令$ {mathcal T} $为Toeplitz运算符$ {T_varphi：L的intfty（S，dsigma）} $的Harde空间$ H ^ 2（S）$生成的$ C ^ ast $-代数$ mathbf {C} ^ n $中的单位范围。众所周知，$ {mathcal T} $包含在$ {T_varphi：运算符名称{VMO} cap L ^ infty（S，dsigma）} $中的基本交换子中。我们证明，$ {T_varphi：运算符名{VMO} cap L ^ infty（S，dsigma）} $中的varphi严格大于$ {mathcal T} $。
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