Toeplitz代数的本质交换子及其性质

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of Operator Theory Pub Date : 2020-02-06 DOI:10.7900/jot.2020feb06.2268

R. Hagger

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引用次数: 8

摘要

我们研究了由具有有界符号的Toeplitz算子在Fock空间Fpα上生成的Toepliz代数。我们证明了Toeplitz代数分别与由带支配、充分局部化和弱局部化算子生成的每个代数一致。此外，我们还确定了它的本质交换子和本质双调和子。对于p=2，这些结果是Xia最近获得的。然而，夏的思想大多与希尔伯特空间理论和方法有关，这些理论和方法不适用于p≠2。相反，我们使用Fulsche最近的一个结果来推广夏的定理。

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Essential commutants and characterizations of the Toeplitz algebra

We study the Toeplitz algebra which is generated by Toeplitz operators with bounded symbols on the Fock space Fpα. We show that the Toeplitz algebra coincides with each of the algebras generated by band-dominated, sufficiently localized and weakly localized operators, respectively. Moreover, we determine its essential commutant and its essential bicommutant. For p=2 these results were obtained recently by Xia. However, Xia's ideas are mostly connected to Hilbert space theory and methods which are not applicable for p≠2. Instead, we use a recent result of Fulsche to generalize Xia's theorems.

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来源期刊

Journal of Operator Theory 数学-数学

CiteScore

1.30

自引率

12.50%

发文量

审稿时长

12 months

期刊介绍： The Journal of Operator Theory is rigorously peer reviewed and endevours to publish significant articles in all areas of operator theory, operator algebras and closely related domains.