Structure of ideals in the space of bounded analytic functions and operator theory

Izuchi(首席研究员)研究了H^∞的理想结构及其上的算子理论，得到了以下结论。1)解决了Suarez在M(H^∞)中涉及平凡点的问题。2)解决了Gorkin和Mortini提出的两个问题，一个是H^∞的闭素理想问题，另一个是极小κ-壳问题。3)表示奇异正测度在M(H^∞)上的“奇性”和“绝对连续性”，并将其应用于研究H^∞+C中的除法问题。4)给出了M(H^∞)中x的一个表示测度的支撑集最大的充分条件。5)用算子范数刻画了H^∞上的复合算子集的连通分支。6)与Nakazi和Seto研究了环面上的后移不变子空间N，并确定了自然两个算子在其上交换的空间N。7)与Yang，确定了向后移位在其上压缩的N，在此基础上，Huruya和Cho研究了对数次正规算子，得到了Riemann-Hilbert问题的解，并解决了Aluthge-Wang关于w-次正规算子核的问题。Matsugu研究了n维球上的解析函数空间，给出了具有Yamashita-Stoll型的加权Bergaman-Privalov空间的特征，并确定了其上的等距关系。Hatori给出了交换Banach代数的环同态的一个表示定理，并给出了环同态为线性的一个条件。Takagi确定了函数代数上加权复合算子的闭值域、本质范数和Hyers-Ulam稳定常数。

Izuchi (head investigator) studied the ideal structure of H^∞ and the operator theory on it, and got the following. 1)Solved Suarez's problem concerned with trivial points in M(H^∞). 2)Solved 2 problems of Gorkin and Mortini, one is concerned with closed prime ideals of H^∞, and another one is minimal κ-hulls. 3)Represented "singularity" and "absolutely continuity" on M(H^∞) of singular positive measures, and applied it to study the division problem in H^∞ + C. 4)Gave a sufficient condition on x in M(H^∞) for which the support set of a representing measure in maximal. 5)Described the connected compornents in the set of composition operators on H^∞ with the operator norm. 6)With Nakazi and Seto, studied backward shift invariant subspaces N on the torus, and determined N on which the natural two operators commute. 7)Wiht Yang, determined N on which the backward shift is contractive.On the results of investigators, Huruya with Cho studied log-hyponormal operators, got a solution of Riemann-Hilbert's problem, and solved Aluthge-Wang's problem concerned with kernels of w-hyponormal operators. Matsugu studied spaces of analytic functions on the n-dimensinal ball, gave a characterization of weighted Bergaman-Privalov spaces with Yamashita-Stoll type, and determined isometries on it. Hatori gave a representation theorem on ring homomorphisms of commutative Banach algebras, and gave a condition for which a ring homomorphism is linear. Takagi determined closed ranges, essential norms, and Hyers-Ulam stability constants of weighted composition operators on function algebras.