HATORI Osamu NIIGATA UNIVERSITY, Faculty of science, Professor, 理学部, 教授 (70156363)
MATSUGU Yasuo Shinsyu University, Faculty of science, Professor, 理学部, 教授 (60020682)
HURUYA Tadashi NIIGATA UNIVERSITY, Faculty of Education and human Sciences, Professor, 教育人間科学部, 教授 (90018648)
TAKAGI Hiroyuki Shinsyu University, Faculty of science, Lecturer, 理学部, 講師 (20206725)
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.