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

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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.