Studies of the structure of operators on analytic function spaces and their invariant subspaces

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Izuchi (head of investigator) got the following results as the joint works.1) Let M be an invariant subspace on the Hardy space over the bidisk. We have multiplication operators R_z and R_w on M. It is given a characterization of M for which rank[R_z, R*_w]=1. Also it is determined N=H^2Θ M satisfying rank[S_z, S*_w]=1.2) It is given a lower and upper bound of the essential norms of the difference of composition operators on the space of bounded analytic functions H∞ on the open unit disk D. Also it is studied the topological structure of weighted composition operators on H∞.3) It is studied quasi-invariant subspaces of the Fock space over C-2 generated by a polynomial.4) It is given a characterization of two Hankel operators on H^2 for which their product is a compact perturbation of Hankel operator.5) It is given a partial answer for Gorkin-Mortini' s problem on closed prime ideals of H∞.6) It is studied a common zero set of equivalent singular inner functions in the maximal ideal space of H∞. Also it is solved two problems on singular inner functions posed by Mortini and Nicolau.Nakazi (investigator) studied a commutant lifting theorem for compression operators.Ohno (investigator) studied compact Hankel-type operators on the space of bounded harmonic functions h∞ on D. Also it is determined the essential norms of difference of composition operators on H∞.