Researches on Properties of the Spaces of Analytic Functions and Their Operators

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(1) S. Ohno, K. Stroethoff and R. Zhao characterized the necessary and sufficient conditions for weighted composition operators to be bounded or compact between Bloch-type spaces of analytic functions on the unit disk including Lipschitz spaces and Bloch spaces. We published a paper. (2) J. S. Choa and S. Ohno investigated the boundedness and compactness of the products of composition and analytic Toepliz Operators. Originally this form is found in the question posed by Deddens and Wong which is concerned with the existence of an analytic Toeplitz operator commuting with a non-zero compact operator. We obtained the results on Hardy and Bergman spaces. This result was published. (3) T. Hosokawa, K. Izuchi and S. Ohno studied properties of the topological space of weighted composition operators on the space of bounded analytic functions on the open unit disk in the uniform operator topology. Moreover, we characterized the compactness of the differences of two weighted composition operators. The paper was accepted and so will be appeared (4) K. Izuchi and S. Ohno investigated Hankel-type operators on the space of bounded harmonic functions on the open unit disk. These operators related to tight uniform algebras, the Dunford-Pettis property, and Bourgain algebras. The paper was accepted and so will be appeared. (5) T. Hosokawa and S. Ohno studied the boundedness and the compactness of the differences of two composition operators on the Bloch and the little Bloch spaces. We proved that the weak compactness of the differences on the little Bloch space is equivalent to the compactness. Moreover we gave attention to the topological structure of the space of composition operators on the Bloch space in the operator topology.