Toeplitz operators associated with analytic crossed products II (invariant subspaces and factorization)

In [16], we introduced the notion of Toeplitz operators associated with analytic crossed products. In this paper, we study the structure of invariant subspaces with respect to the analytic crossed products. We also investigate the inner-outer factorization problems for analytic Toeplitz operators, the factorization problem for non-negative Toeplitz operators and Szegö's infimum problem.This work was supported in part by a Grant-in-Aid for Scientific Research from the Japanese Ministry of Education.