Fares, Tonie; Lefèvre, Pascal Nuclear composition operators on Bloch spaces. (English) Zbl 1442.47013 Proc. Am. Math. Soc. 148, No. 6, 2487-2496 (2020). Summary: We characterize the nuclear composition operators \(C_\varphi f=f\circ \varphi\) on the classical and little Bloch spaces. In addition, we construct an example of a conformal mapping of the unit disk \(\mathbb{D}\) into itself which has a contact point with the unit circle \(\mathbb{T}\), and induces a nuclear composition operator. Cited in 2 ReviewsCited in 3 Documents MSC: 47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.) 47B33 Linear composition operators 30H30 Bloch spaces 46E15 Banach spaces of continuous, differentiable or analytic functions PDFBibTeX XMLCite \textit{T. Fares} and \textit{P. Lefèvre}, Proc. Am. Math. Soc. 148, No. 6, 2487--2496 (2020; Zbl 1442.47013) Full Text: DOI References: [1] Arendt, Wolfgang; Chalendar, Isabelle; Kumar, Mahesh; Srivastava, Sachi, Asymptotic behaviour of the powers of composition operators on Banach spaces of holomorphic functions, Indiana Univ. Math. J., 67, 4, 1571-1595 (2018) · Zbl 06971428 [2] Cowen, Carl C.; MacCluer, Barbara D., Composition operators on spaces of analytic functions, Studies in Advanced Mathematics, xii+388 pp. (1995), CRC Press, Boca Raton, FL · Zbl 0873.47017 [3] Diestel, Joe; Jarchow, Hans; Tonge, Andrew, Absolutely summing operators, Cambridge Studies in Advanced Mathematics 43, xvi+474 pp. (1995), Cambridge University Press, Cambridge · Zbl 0855.47016 [4] Duren, Peter; Schuster, Alexander, Bergman spaces, Mathematical Surveys and Monographs 100, x+318 pp. (2004), American Mathematical Society, Providence, RI · Zbl 1059.30001 [5] Hedenmalm, Haakan; Korenblum, Boris; Zhu, Kehe, Theory of Bergman spaces, Graduate Texts in Mathematics 199, x+286 pp. (2000), Springer-Verlag, New York · Zbl 0955.32003 [6] Lusky, Wolfgang, On the isomorphism classes of weighted spaces of harmonic and holomorphic functions, Studia Math., 175, 1, 19-45 (2006) · Zbl 1114.46020 [7] Lef\`evre, Pascal; Rodr\'{\i}guez-Piazza, Luis, Absolutely summing Carleson embeddings on Hardy spaces, Adv. Math., 340, 528-587 (2018) · Zbl 1475.30117 [8] Madigan, Kevin; Matheson, Alec, Compact composition operators on the Bloch space, Trans. Amer. Math. Soc., 347, 7, 2679-2687 (1995) · Zbl 0826.47023 [9] Montes-Rodr\'{\i}guez, Alfonso, The essential norm of a composition operator on Bloch spaces, Pacific J. Math., 188, 2, 339-351 (1999) · Zbl 0932.30034 [10] Pommerenke, Ch., Boundary behaviour of conformal maps, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 299, x+300 pp. (1992), Springer-Verlag, Berlin · Zbl 0762.30001 [11] Shapiro, Joel H., Composition operators and classical function theory, Universitext: Tracts in Mathematics, xvi+223 pp. (1993), Springer-Verlag, New York · Zbl 0791.30033 [12] Shapiro, J. H.; Taylor, P. D., Compact, nuclear, and Hilbert-Schmidt composition operators on \(H^2 \), Indiana Univ. Math. J., 23, 471-496 (1973/74) · Zbl 0276.47037 [13] Wojtaszczyk, P., Banach spaces for analysts, Cambridge Studies in Advanced Mathematics 25, xiv+382 pp. (1991), Cambridge University Press, Cambridge · Zbl 0724.46012 [14] Zhu, Ke He, Bloch type spaces of analytic functions, Rocky Mountain J. Math., 23, 3, 1143-1177 (1993) · Zbl 0787.30019 [15] Zhu, Kehe, Operator theory in function spaces, Mathematical Surveys and Monographs 138, xvi+348 pp. (2007), American Mathematical Society, Providence, RI · Zbl 1123.47001 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.