Complex symmetry of weighted composition operators in several variables
Complex symmetry of weighted composition operators in several variables
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DOI：
10.1142/s0129167x16500178
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发表时间：
2016-02
影响因子：
0.6
通讯作者：
Maofa Wang;Xingxing Yao
中科院分区：
文献类型：
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作者：
Maofa Wang;Xingxing Yao
在本文中，我们研究了当加权复合算子Cψ,φ在一般函数空间Hs上复对称时的解析符号ψ和φ。作为应用，我们完整地刻画了复对称加权合成算子的紧致性、正态性和等距性。特别是，我们证明了紧致性和希尔伯特-施密特性的等价性，以及此类算子的非正态复对称算子的存在性，这回答了 Noor 在 [关于 H2(𝔻) 上的复对称组合算子的一个例子，J. Funct.] 中提出的一个开放问题。肛门。 269 (2015) 1899–1901] 对于高维情况。
In this paper, we investigate analytic symbols ψ and φ when the weighted composition operator Cψ,φ is complex symmetric on general function space Hs. As applications, we characterize completely the compactness, normality and isometry of complex symmetric weighted composition operators. Especially, we show that the equivalence of compactness and Hilbert–Schmidtness, and the existence of non-normal complex symmetric operators for such operators, which answers one open problem raised by Noor in [On an example of a complex symmetric composition operators on H2(𝔻), J. Funct. Anal. 269 (2015) 1899–1901] for higher dimensional case.