Hassanloo, Mostafa Estimates of norm and essential norm of differences of differentiation composition operators on weighted Bloch spaces. (English) Zbl 1474.47061 Sahand Commun. Math. Anal. 17, No. 1, 109-124 (2020). Summary: Norm and essential norm of differences of differentiation composition operators between Bloch spaces have been estimated in this paper. As a result, we find characterizations for boundedness and compactness of these operators. MSC: 47B33 Linear composition operators 30H30 Bloch spaces 47B38 Linear operators on function spaces (general) Keywords:differentiation composition operators; weighted Bloch spaces; essential norm PDFBibTeX XMLCite \textit{M. Hassanloo}, Sahand Commun. Math. Anal. 17, No. 1, 109--124 (2020; Zbl 1474.47061) Full Text: DOI References: [1] J. Bonet, M. Lindstrom and E. Wolf,Differences of Composition operators between weighted Banach spaces of holomorphic functions, J. Aust. Math. Soc., 84 (2008), pp. 9-20. · Zbl 1145.47020 [2] C.C. Cowen and B.D. Maccluer,Composition operators on spaces of analytic functions, CRC Press, Boca Raton, 1995. · Zbl 0873.47017 [3] J. Dai and C. Ouyang,Differences of weighted composition cperators onHα∞(BN), J. Ineq. Appl., 2009 (2009), pp. 1-20. [4] T. Hosokawa and S. Ohno,Differences of composition operators on the Bloch spaces, J. Operator Theory, 57 (2), (2007), pp. 229-242. · Zbl 1174.47019 [5] T. Hosokawa and S. Ohnol,Differences of weighted composition operators acting from Bloch space toH1, Tran. Amer. Math. Soc., 363 (2011), pp. 5321-5340. · Zbl 1231.47023 [6] S. Li,Differences of generalized composition operators on the Bloch space, J. Math. Anal. Appl., 394 (2012), pp. 706-711. · Zbl 1266.47044 [7] S. Li and S. Stevic,Generalized weighted composition operators from a-Bloch spaces into weighted-type spaces, J. Inequal. Appl., 2015:265 (2015), pp. 1-12. · Zbl 1338.47018 [8] H. Li and X. Fua,New characterization of generalized weighted composition operators from the bloch space into the zygmund space, J. Funct. Spaces Appl., 2013 (2013), 6 pages. [9] X. Liu and S. Li,Differences of generalized weighted composition operators from the bloch space into bers-type spaces, Filomati, 31 (2017), pp. 1671-1680. [10] B. MacCluer, S. Ohno and R. Zhao,Topological structure of the space of composition operators onH1, Integ. Equ. Operator Theory, 40 (2001), pp. 481-494. · Zbl 1062.47511 [11] J. Moorhouse,Compact differences of composition operators, J. Funct. Anal., 219 (2008), pp. 70-92. · Zbl 1087.47032 [12] P. Nieminen,Compact differences of composition operators on Bloch and lipschitz spaces, Comput. Methods Funct. Theory, 7 (2007), pp. 325-344. · Zbl 1146.47016 [13] J.H. Shapiro,Composition operator and classical function theory, Springer, New York, 1993. · Zbl 0791.30033 [14] E. Wolf,Compact differences of composition operators, Bull. Austral. Math. Soc., 77 (2008), pp. 161-165. · Zbl 1137.47020 [15] W. Yang and X. Zhu,Differences of generalized weighted composition operators between growth spaces, Annales Polonici Mathematici, 112 (2014), 67-83. · Zbl 1309.47026 [16] K. Yang and Z. Zhou,Essential norm of the difference of composition operators on bloch space, Czechoslovak Math. J., 60 (2010), pp. 1139-1152. · Zbl 1220.47045 [17] X. Zhu,Generalized weighted composition operators on Bloch-type spaces, J. Inequal. Appl., 2015:59 (2015). · Zbl 1309.47027 [18] X. Zhu,Essential norm of generalized weighted composition operators on Bloch-type spaces, Appl. Math. Comput., 274 (2016), pp. 133-142. · Zbl 1410.30032 [19] K. Zhu,Boch type spaces of analytic functions, Rocky Mountain J. Math., 23 (1993), pp. 1143-1177. · Zbl 0787.30019 [20] K. Zhu,Spaces of holomorphic functions in the unit Ball. Springer, New York, 2005. · Zbl 1067.32005 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.