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2017 Fiscal Year Final Research Report

Researches on the structures of analytic function spaces and linear operators on them

Research Project

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Project/Area Number 15K04905
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionNippon Institute of Technology

Principal Investigator

OHNO Shuichi  日本工業大学, 工学部, 准教授 (20265367)

Co-Investigator(Kenkyū-buntansha) 泉池 敬司  新潟大学, 自然科学系, フェロー (80120963)
細川 卓也  茨城大学, 工学部, 准教授 (90553579)
Project Period (FY) 2015-04-01 – 2018-03-31
Keywords合成作用素 / 荷重合成作用素 / Toeplitz作用素 / Hardy空間 / Bergman空間 / Bloch空間
Outline of Final Research Achievements

We have characterized the asymptotic Toeplitzness associated with weighted composition operators on the Hardy-Hilbert space in the uniform operator, strong and weak topologies. Indeed, the non-trivial uniformly asymptotically Toeplitzness is equivalent to the compactness of the weighted composition operator. Also, we have considered the hyperbolic derivatives of products of analytic self-maps of the unit disk and so provided explicit examples of products that induce compact composition operators on Bloch and little Bloch spaces.

Free Research Field

数物系科学

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Published: 2019-03-29  

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