Dixmier Trace for Toeplitz Operators on Symmetric Domains
Dixmier Trace for Toeplitz Operators on Symmetric Domains
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DOI：
10.1016/j.jfa.2016.04.022
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发表时间：
2015-08
期刊：
影响因子：
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通讯作者：
H. Upmeier;Kai Wang
中科院分区：
文献类型：
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作者：
H. Upmeier;Kai Wang
对于高阶有界对称域上的Toeplitz算子，没有明显的方法来定义Toeplitz C -代数中的Dixmier轨迹，因为对易子通常是不紧的。本文通过构造一个Hilbert商模来解决这一问题，该模对应于长度为1的分区，该分区导致macev类中的换易子ln，∞。我们还得到了这类换向子的Dixmier迹在底层边界几何中的显式表达式，其中涉及到一种用Jordan理论术语定义的新型标志流形。
For Toeplitz operators on bounded symmetric domains of higher rank, there is no obvious way to define the Dixmier trace within the Toeplitz C⁎-algebra, since commutators are in general not compact. In this paper we solve this problem by constructing a Hilbert quotient module, corresponding to partitions of length 1, which leads to commutators in the Macaev class L n,∞. We also obtain an explicit formula for the Dixmier trace of such commutators in terms of the underlying boundary geometry, which involves a new type of flag manifold defined in Jordan theoretic terms.