学术报告（卢玉峰 2024.7.4）

摘要： Due to the relation with the invariant subspace problem, the structure of compressed shift operator S_z is one of the important problems in operator theory.  This talk focuses on the reducibility of the compressed shift operator on the Hardy space over the bidisk via the geometric approach. We introduce Alger reducibility and pure isometry reducibility, calculate the spectrum and essential spectrum of on the Beurling type quotient modules induced by rational inner functions, and give a complete characterization for S_z^* to be a Cowen-Douglas operator. Then we extend the notion of Cowen-Douglas operator to be the generalized Cowen-Douglas operator, and the connection between the reducibility of S_z and generalized Cowen-Douglas operator are established. By using the geometric approach, we also study the reducing subspaces of S_z on certain polynomial quotient modules.