AI 中文总结
本文刻画向量值Hardy空间上Toeplitz与Hankel算子互为斜交换子的条件及乘积自伴的充要条件，分类了单侧移位算子及其伴随算子的斜交换子，推广了已有相关结果。
AI 中文摘要
本文刻画了向量值Hardy空间上的Toeplitz算子与Hankel算子互为斜交换子的条件，确定了它们的乘积为自伴算子的充要条件，这些刻画推广了文献\uc11b{LZD}中的结果。此外，本文完全分类了单侧移位算子$S$、其伴随算子$S^*$及$S\bigoplus S^*$的斜交换子，还刻画了以$S$、$S^*$及$S\bigoplus S^*$为斜交换子的有界线性算子类。
英文摘要
In this article, we characterize when a Toeplitz operator and a Hankel operator on the vector-valued Hardy space are skew commutators of each other, and determine necessary and sufficient conditions under which their product is self-adjoint. These characterizations extend the results in \cite{LZD}. In addition, we completely classify the skew commutators of the unilateral shift $S$, its adjoint $S^*$ and $S\oplus S^*.$ We also characterize the class of bounded linear operators that have $S$, $S^*$ and $S\oplus S^*$ as skew-commutators.
Comments24 pages
