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

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04905
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Nippon 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