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

1)设M是双圆盘上Hardy空间上的不变子空间。在M上有乘法算子R_z和R_w，给出了M的秩为[R_z，R*_w]=1的刻画，并确定了N=H^2ΘM满足秩为[S_z，给出了开单位圆盘D上有界解析函数H-∞空间上复合算子差的本质范数的一个上下界，并研究了H-∞上加权复合算子的拓扑结构。3)研究了C-2上由多项式生成的Fock空间的拟不变子空间。4)给出了H^2上两个乘积是Hankel算子的紧扰动的Hankel算子的刻画。5)部分回答了Gorkin-Mortini的S问题关于H∞的闭素理想。6)在H∞的极大理想空间中研究了等价奇异内函数的公共零集。Nakazi研究了压缩算子的一个交换提升定理，Ohno研究了D上有界调和函数空间h∞上的紧Hankel型算子，并确定了H∞上复合算子差的本质范数.

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∞.