论文标题
阿贝尔群体的力矩地图，并通勤在单位球上行动的托管操作员
Moment maps of Abelian groups and commuting Toeplitz operators acting on the unit ball
论文作者
论文摘要
我们证明，对于单位球$ \ mathbb {b}^n $的每个连接的Abelian亚组$ h $，我们可以将一组有界符号关联，其相应的Toeplitz操作员会产生一个交换性的$ C^**$ - 在每个举重Bergman空间上的algebra。这些符号是$ a（z）= f（μ^h（z））$的表格，其中$μ^h $是$ h $在$ \ mathbb {b}^n $上的动作的力矩映射。我们表明，对于这种结构，如果$ h $是最大的阿贝尔亚组，那么所引入的符号正是$ h $ invariant符号。我们提供了矩图的明确计算，以获取在坐标方面描述的特殊符号集。特别是，证明我们的符号集具有特定情况，所有符号集都来自当前文献中的所有符号集，这些符号集产生了toeplitz operator在单位球上所有加权伯格曼空间上产生交换性$ c^*$ - 代数 - 代数$ \ mathbb {b}^n $。此外，我们展示的例子表明，这项工作中介绍的一些符号集尚未考虑过。最后，介绍了Toeplitz运算符的相应光谱的几个明确公式。这些包括光谱积分表达式，简化了单位球的最大Abelian亚组的已知公式。
We prove that to every connected Abelian subgroup $H$ of the biholomorphisms of the unit ball $\mathbb{B}^n$ we can associate a set of bounded symbols whose corresponding Toeplitz operators generate a commutative $C^*$-algebra on every weighted Bergman space. These symbols are of the form $a(z) = f(μ^H(z))$, where $μ^H$ is the moment map for the action of $H$ on $\mathbb{B}^n$. We show that, for this construction, if $H$ is a maximal Abelian subgroup, then the symbols introduced are precisely the $H$-invariant symbols. We provide the explicit computation of moment maps to obtain special sets of symbols described in terms of coordinates. In particular, it is proved that our symbol sets have as particular cases all symbol sets from the current literature that yield Toeplitz operators generating commutative $C^*$-algebras on all weighted Bergman spaces on the unit ball $\mathbb{B}^n$. Furthermore, we exhibit examples that show that some of the symbol sets introduced in this work have not been considered before. Finally, several explicit formulas for the corresponding spectra of the Toeplitz operators are presented. These include spectral integral expressions that simplify the known formulas for maximal Abelian subgroups for the unit ball.
