勷勤数学•专家报告

题      目：Reducing subspaces of the Bergman space

报  告  人： 罗率兵 副教授  (邀请人：黄志波)

                                   湖南大学

时      间： 7月8日  16：00-17:00

地     点：数科院东楼401

报告人简介:

       罗率兵，湖南大学数学学院副教授，研究方向为算子理论与复分析。博士毕业于田纳西大学。曾在纽芬兰纪念大学做博士后，合作导师为肖杰教授。 在Adv. Math., JFA, Sci. China Math., J. Lond. Math. Soc., Math. Z., Canad. J. Math.等期刊上发表过论文。现主持一项国家自然科学基金面上项目和湖南省杰出青年基金项目。

摘      要：

       Suppose $T$ is a bounded linear operator on a Hilbert space $\mathcal{H}$, if a closed subspace $\mathcal{M}$ of $\mathcal{H}$ is invariant under both $T$ and $T^*$, then $\mathcal{M}$ is called a reducing subspace of $T$ on $\mathcal{H}$. Reducing subspaces of $M_B$ on the Bergman space $L_a^2(\mathbb{D})$ have been studied extensively in the past, where $B$ is a finite Blaschke product. Through many experts' efforts, it is proven that the von Neumann algebra $\mathcal{V}^*(B) =\{M_B,M_B^*\}'$ is abelian, and the number of minimal reducing subspaces of $M_B$ on $L_a^2(\mathbb{D})$ is equal to the number of minimal projections in $\mathcal{V}^*(B)$, which is also equal to the components of the Riemann surface $\mathcal{S}_B$. However, determining this integer for a specific finite Blaschke product $B$ is a challenging task. In this talk, we discuss how to attack this problem when the order of $B$ is small.

          欢迎老师、同学们参加、交流！