论文标题
对称polydisc上的Toeplitz运营商和希尔伯特模块
Toeplitz operators and Hilbert modules on the symmetrized polydisc
论文作者
论文摘要
$ \ MATHSF S $ -TOEPLITZ操作员的收集何时相对于通勤有限操作员的元组$ \ Mathsf S =（S_1，S_1，S_2，\ ldots，S_ {D-1}，P）$，这是Symmetrized Polydisc作为光谱集合的频谱，非企业？答案是根据$ p $的权力以及统一的延伸。在途中，研究了棕色半岛关系。建立了换向的提升定理。最后，我们建立了一个连接由$ \ Mathsf S $和其统一分机$ \ Mathsf r $的通勤者生成的$ c^*$ - 代数的一般结果。
When is the collection of $\mathsf S$-Toeplitz operators with respect to a tuple of commuting bounded operators $\mathsf S= (S_1, S_2, \ldots , S_{d-1}, P)$, which has the symmetrized polydisc as a spectral set, non-trivial? The answer is in terms of powers of $P$ as well as in terms of a unitary extension. En route, Brown-Halmos relations are investigated. A commutant lifting theorem is established. Finally, we establish a general result connecting the $C^*$-algebra generated by the commutant of $\mathsf S$ and the commutant of its unitary extension $\mathsf R$.
