论文摘要
本篇硕士论文主要研究单位多圆盘Bergman空间的正交补空间上的对偶Toeplitz算子，着重考虑了对偶Toeplitz算子的交换性，本质交换性，代数结构。主要是通过其与Toeplitz算子，Hankel算子的紧密关系及多复变函数论来完成的。第一章对相关的研究背景进行了概述，并给出一些基本概念及符号，最后说明了研究意义。第二章刻画了以有界多重调和函数为符号的对偶Toeplitz算子的交换性。证明了SφSψ=SψSφ当且仅当φ和ψ满足下列情形之一：（1）φ和ψ在Dn上均解析。（2） （?）和（?）在Dn上均解析。（3）存在两个不全为零的常数A，B，使得Aφ+Bψ在Dn上是常值。第三章分别刻画了以有界可测函数和有界多重调和函数为符号的对偶Toeplitz算子的本质交换性。在前者情形下，得到了TfTg－TgTf是紧的当且仅当‖（Hgkω）（?）(H?kω)-（Hfkω）（?）(H?kω)‖→0，ω→αDn。在后者情形下，得到了与以往经典结果相似的结论。第四章证明了对偶Toeplitz代数I（C（（?）））的半换位理想是紧算子全体，并研究了其代数结构，成立短正合序列（0）→semiI（L∞（Dn））→I（L∞（Dn））→L∞（Dn）→（0）。
论文目录
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