Products of Toeplitz Operators on the Bergman Space
Products of Toeplitz Operators on the Bergman Space
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DOI：
10.1090/s1061-0022-06-00945-9
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发表时间：
2006-04
影响因子：
0.8
通讯作者：
I. Louhichi;E. Strouse;Lova Zakariasy
中科院分区：
文献类型：
--
作者：
I. Louhichi;E. Strouse;Lova Zakariasy
摘要。1962年布朗和哈尔莫斯给出了简单的条件的产品的两个Toeplitz运营商的哈代空间是等于一个Toeplitz运营商。最近，Ahern和Cucković证明了Bergman空间上具有有界调和符号的Toeplitz算子的类似结果。对于一般符号，情况要复杂得多。我们给出了乘积是Toeplitz算子的充分必要条件（定理6.1），在某些情况下给出了乘积符号的显式公式（定理6.4），然后证明了几乎任何事情都可能发生（定理6.7）。
Abstract.In 1962 Brown and Halmos gave simple conditions for the product of two Toeplitz operators on Hardy space to be equal to a Toeplitz operator. Recently, Ahern and Cucković showed that a similar result holds for Toeplitz operators with bounded harmonic symbols on Bergman space. For general symbols, the situation is much more complicated. We give necessary and sufficient conditions for the product to be a Toeplitz operator (Theorem 6.1), an explicit formula for the symbol of the product in certain cases (Theorem 6.4), and then show that almost anything can happen (Theorem 6.7).