The compressed shift operators on Hardy space over bidisk

In this talk, we will give the reducibility of the compressed shift operator on the Hardy space over the bidisk via the geometric approach. we extend the notion of Cowen-Douglas operator to be the generalized Cowen-Douglas operator, and the connection between the reducibility of and generalized Cowen-Douglas operator are established. The motivation to focus on these problems is to solve the invariant subspace problem.

12.10.pdf