Trace ideal criteria for Toeplitz operators
Trace ideal criteria for Toeplitz operators
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DOI：
10.1016/0022-1236(87)90072-3
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发表时间：
1987-08
影响因子：
1.7
通讯作者：
D. Luecking
中科院分区：
文献类型：
--
作者：
D. Luecking
对于开单位圆盘U上的复测度μ，在解析函数的Hilbert空间H上定义一个算子T μ，其再生核为k（z，w）.对于一定规模的Hilbert空间H α，α< 1，其中包括哈代空间H2和加权Bergman空间A2，β，得到了T μ属于Schatten理想Sp的条件.如果μ是正测度，则这些条件是充要的.应用复合算子和限制算子的指示。
For a complex measure μ on the open unit disk U define an operator T μ on a Hilbert space H of analytic functions with reproducing kernel k (z, w) by u. For a certain scale of Hilbert spaces H α, α< 1, which includes the Hardy space H 2 and weighted Bergman spaces A 2, β, conditions are obtained which imply T μ belongs to a Schatten ideal S p. If μ is a positive measure then these conditions are necessary and sufficient. Application to composition operators and restriction operators are indicated.