加权复合算子从Bloch型空间到圆盘代数的拓扑结构

doi:10.12052/gdutxb.200092

Journal of Guangdong University of Technology ›› 2021, Vol. 38 ›› Issue (03): 62-64.doi: 10.12052/gdutxb.200092

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The Topological Structure of Weighted Composition Operators from Bloch Type Spaces to the Disk Algebra

Xu Li-kui, Deng Xiu-qin, Liu Jun-ming

School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China

Received:2020-07-22 Online:2021-05-10 Published:2021-03-12

Abstract

Abstract: Let $ A$ be the disk algebra, $ u$ and $ \varphi $ be analytic functins on A, some estimates of weighted composition operators $ u{C_\varphi }$ from Bloch type spaces to the disk algebra are characterized. At the same time, the path connectedness of the space of weighted composition operators is investigated and a conclusion is derived that any two bounded weighted composition operators are pathwise connected.

Key words: topological structure, weighted composition operators, Bloch type spaces, disk algebra, path connectedness

CLC Number:

O174.5

Xu Li-kui, Deng Xiu-qin, Liu Jun-ming. The Topological Structure of Weighted Composition Operators from Bloch Type Spaces to the Disk Algebra[J].Journal of Guangdong University of Technology, 2021, 38(03): 62-64.

References

[1] ZHU K. Bloch type spaces of analytic functions [J]. The Rocky Mountain Journal of Mathematics, 1993, 23(3): 1143-1177.
[2] ZHU K. Operator theory in function spaces[M]. 2nd ed. Providence: Mathematical Surveys and Monographs, 2007.
[3] CONTRERAS M D, HERNÁNDEZ-DÍAZ A G. Weighted composition operators on Hardy spaces [J]. Journal of Mathematical Analysis and Applications, 2001, 263(1): 224-233.
[4] ČUČKOVIÓ Z, ZHAO R. Weighted composition operators on the Bergman space [J]. Journal of the London Mathematical Society, 2004, 70(2): 499-511.
[5] IZUCHI K, OHNO S. Topological structure of the space of weighted composition operators between different Hardy spaces [J]. Integral Equations Operator Theory, 2014, 80(2): 153-164.
[6] HOSOKAWA T, IZUCHI K, ZHENG D. Isolated points and essential components of composition operators on H^∞ [J]. Proceeding of the American Mathematical Society, 2002, 130(6): 1765-1773.
[7] FANG Z, ZHOU Z. The topological structure of weighted composition operators from Lipschitz spaces to H^∞ [J]. Bulletin of the Malaysian Mathematical Sciences Society, 2019, 42(3): 897-908.
[8] 张学军. C ⁿ中单位球上几个全纯函数空间上加权复合算子的有界性[J]. 数学研究, 2003, 36(3): 243-250.
ZHANG X J. Boundedness of weighted composition operators on -Bloch spaces on the unit ball of C ⁿ [J]. Journal of Mathematical Study, 2003, 36(3): 243-250.
[9] MANHAS J, ZHAO R. New estimates of essential norms of weighted composition operators between Bloch type spaces [J]. Journal of Mathematical Analysis and Applications, 2012, 389(1): 32-47.

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