加权Bloch空间上复合算子的线性组合

张利, 楚秀娇

数学学报 ›› 2021, Vol. 64 ›› Issue (1) : 139-144.

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数学学报 ›› 2021, Vol. 64 ›› Issue (1) : 139-144. DOI: 10.12386/A2021sxxb0011
论文

加权Bloch空间上复合算子的线性组合

    张利, 楚秀娇
作者信息 +

Linear Combinations of Composition Operators on Weighted Bloch Type Space

    Li ZHANG, Xiu Jiao CHU
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文章历史 +

摘要

λii=1,…,N)是一列非0的数,D是一维复平面C的开单位圆盘,φii=1,…,N)是D的解析自映射,本文研究了定义在加权Bloch空间上复合算子线性组合∑i=1N λiCφi的紧致性.

Abstract

For i=1, 2, …, N, let λi be nonzero number, and D the unit open disk of complex plane C, φi is analytic self-maps of D. In this paper, the compactness of linear combinations of composition operators ∑i=1N λiCφi on the weighted Bloch space is discussed.

关键词

加权Bloch空间 / 复合算子 / 线性组合 / 紧致性

Key words

weighted Bloch space / composition operator / linear combinations / compactness

引用本文

导出引用
张利, 楚秀娇. 加权Bloch空间上复合算子的线性组合. 数学学报, 2021, 64(1): 139-144 https://doi.org/10.12386/A2021sxxb0011
Li ZHANG, Xiu Jiao CHU. Linear Combinations of Composition Operators on Weighted Bloch Type Space. Acta Mathematica Sinica, Chinese Series, 2021, 64(1): 139-144 https://doi.org/10.12386/A2021sxxb0011

参考文献

[1] Cowen C. C., MacCluer B. D., Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, FL, 1995.
[2] Hosokawa T., Nieminen P. J., Ohno S., Linear combinations of composition operators on the Bloch spaces, Canad. J. Math., 2011, 63(4):862-877.
[3] Hosokawa T., Ohno S., Differences of composition operators on the Bloch spaces, J. Operator Theory, 2007, 57(2):229-242.
[4] Izuchi K., Ohno S., Linear combinations of composition operators on H, J. Math. Anal. Appl., 2008, 338:820-839.
[5] Kellay K., Lefèvre P., Compact composition operators on weighted Hilbert spaces of analytic functions, J. Math. Anal. Appl., 2012, 386:718-727.
[6] Koo H., Wang M. F., Cancellation properties of composition operators on Bergman spaces, J. Math. Anal. Appl., 2015, 432:1174-1182.
[7] Lindström M., Saukko E., Essential norm of weighted composition operators and difference of composition operators between standard weighted Bergman spaces, Complex Anal. Oper. Theory, 2015, 9:1411-1432.
[8] Lou Z. J., Composition operator on Bloch type spaces, Analysis, 2003, 1(1):81-95.
[9] Nieminen P., Compact differences of composition operators on Bloch and Lipschitz spaces, Comput. methods Funct. Theory, 2007, 7(2):325-344.
[10] Schwartz H. J., Composition Operators on Hp, Ph.D. Thesis, University of Toledo, Toledo, 1969.
[11] Shapiro J. H., Composition Operators and Classical Function Theory, Springer-Verlag, New York, 1993.
[12] Shi Y. C., Li S. X., Differences of composition operators on Bloch type spaces, Complex Anal. Oper. Theory, 2017, 11:227-242.
[13] Shi Y. C., Li S. X., Linear combination of composition operators on H and the Bloch space, Arch. Math., 2019, 112:511-519.
[14] Zhang L., Zhou Z. H., Topological structure of the space of composition operators from F (p, q, s) space to Bμ space, Taiwanese J. Math., 2014, 18(1):285-304.
[15] Zhu K. H., Operator Theory in Function Spaces, Marcel Dekker Inc., New York, 1990.

基金

国家自然科学基金资助项目(11526116);南阳师范学院自然科学基金资助项目(QN2017047)

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