Shi, Yecheng; Li, Songxiao; Zhu, Xiangling Difference of weighted composition operators from \(H^\infty\) to the Bloch space. (English) Zbl 1469.30108 Bull. Iran. Math. Soc. 47, No. 4, 1245-1259 (2021). Summary: Some new characterizations for the boundedness and compactness of the difference of two weighted composition operators acting from \(H^\infty\) to the Bloch space are given in this paper. MSC: 30H05 Spaces of bounded analytic functions of one complex variable 30H30 Bloch spaces 47B33 Linear composition operators Keywords:\(H^\infty\); Bloch space; weighted composition operator PDFBibTeX XMLCite \textit{Y. Shi} et al., Bull. Iran. Math. Soc. 47, No. 4, 1245--1259 (2021; Zbl 1469.30108) Full Text: DOI arXiv References: [1] Acharyya, S.; Wu, Z., Compact and Hilbert-Schmidt differences of weighted composition operators, Integral Equ. Oper. Theory, 88, 465-482 (2017) · Zbl 1466.47019 [2] Berkson, E., Composition operators isolated in the uniform operator topology, Proc. Am. Math. Soc., 81, 230-232 (1981) · Zbl 0464.30027 [3] Goebeler, T., Composition operators acting between Hardy spaces, Integral Equ. Oper. Theory, 41, 389-395 (2001) · Zbl 0997.47021 [4] Hu, Q.; Li, S.; Shi, Y., A new characterization of differences of weighted composition operators on weighted-type spaces, Comput. Methods Funct. Theory, 17, 303-318 (2017) · Zbl 1432.30042 [5] Hosokawa, T., Differences of weighted composition operators on the Bloch spaces, Complex Anal. Oper. Theory, 3, 847-866 (2009) · Zbl 1216.47037 [6] Hosokawa, T.; Ohno, S., Differences of composition operators on the Bloch spaces, J. Oper. Theory, 57, 229-242 (2007) · Zbl 1174.47019 [7] Hosokawa, T.; Ohno, S., Differences of weighted composition operators acting from Bloch space to \(H^\infty \), Trans. Am. Math. Soc., 363, 5321-5340 (2011) · Zbl 1231.47023 [8] Hosokawa, T.; Ohno, S., Differences of weighted composition operators from \(H^\infty\) to Bloch space, Taiwan. J. Math., 16, 2093-2105 (2012) · Zbl 1283.47038 [9] Li, S., Differences of generalized composition operators on the Bloch space, J. Math. Anal. Appl., 394, 706-711 (2012) · Zbl 1266.47044 [10] Maccluer, B.; Ohno, S.; Zhao, R., Topological structure of the space of composition operators on \(H^\infty \), Integral Equ. Oper. Theory, 40, 481-494 (2001) · Zbl 1062.47511 [11] Moorhouse, J., Compact differences of composition operators, J. Funct. Anal., 219, 70-92 (2005) · Zbl 1087.47032 [12] Nieminen, P., Compact differences of composition operators on Bloch and Lipschitz spaces, Comput. Method Funct. Theory, 7, 325-344 (2007) · Zbl 1146.47016 [13] Nieminen, P.; Saksman, E., On compactness of the difference of composition operators, J. Math. Anal. Appl., 298, 501-522 (2004) · Zbl 1072.47021 [14] Ohno, S., Weighted composition operators between \(H^\infty\) and the Bloch space, Taiwan. J. Math., 5, 555-563 (2001) · Zbl 0997.47025 [15] Saukko, E., Difference of composition operators between standard weighted Bergman spaces, J. Math. Anal. Appl., 381, 789-798 (2011) · Zbl 1244.47024 [16] Saukko, E., An application of atomic decomposition in Bergman spaces to the study of differences of composition operators, J. Funct. Anal., 262, 3872-3890 (2012) · Zbl 1276.47032 [17] Shapiro, J.; Sundberg, C., Isolation amongst the composition operators, Pac. J. Math., 145, 117-152 (1990) · Zbl 0732.30027 [18] Shi, Y.; Li, S., Essential norm of the differences of composition operators on the Bloch space, Math. Inequal. Appl., 20, 543-555 (2017) · Zbl 1375.30090 [19] Shi, Y.; Li, S., Differences of composition operators on Bloch type spaces, Complex Anal. Oper. Theory., 11, 227-242 (2017) · Zbl 1361.30098 [20] Shi, Y.; Li, S., Linear combination of composition operators on \(H^\infty\) and the Bloch space, Archiv der Math., 112, 511-519 (2019) · Zbl 1426.30043 [21] Wulan, H.; Zheng, D.; Zhu, K., Compact composition operators on BMOA and the Bloch space, Proc. Am. Math. Soc., 137, 3861-3868 (2009) · Zbl 1194.47038 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.