Eigenvalue Characterization of Radial Operators on Weighted Bergman Spaces Over the Unit Ball
Eigenvalue Characterization of Radial Operators on Weighted Bergman Spaces Over the Unit Ball
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DOI：
10.1007/s00020-013-2101-1
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发表时间：
2014-02
影响因子：
0.8
通讯作者：
W. Bauer;Crispin Herrera Yañez;N. Vasilevski
中科院分区：
文献类型：
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作者：
W. Bauer;Crispin Herrera Yañez;N. Vasilevski
研究了作用于单位球上的标准加权Bergman空间的径向算子，特别是径向Toeplitz算子。它们对于标准单项式基是对角的，并且它们的特征值序列的元素仅依赖于枚举基元素的多索引的长度。通过给出经典Hausdorff矩问题的加权扩展，明确刻画了径向Toeplitz算子的特征值序列，并证明了所有具有有界可测径向符号的径向Toeplitz算子集合的范数闭包与由这些Toeplitz算子生成的c *-代数一致，并且与在Schmidt意义上缓慢振荡的序列的c *-代数同构等距。
We study the so-called radial operators, and in particular radial Toeplitz operators, acting on the standard weighted Bergman space on the unit ball in. They turn out to be diagonal with respect to the standard monomial basis, and the elements of their eigenvalue sequences depend only on the length of multi-indexes enumerating basis elements. We explicitly characterize the eigenvalue sequences of radial Toeplitz operators by giving a solution for the weighted extension of the classical Hausdorff moment problem, and show that the norm closure of the set of all radial Toeplitz operators with bounded measurable radial symbols coincides with theC*-algebra generated by these Toeplitz operators and is isomorphic and isometric to theC*-algebra of sequences that slowly oscillate in the sense of Schmidt.