COMPOSITION OPERATORS ON FINITE RANK MODEL SUBSPACES
Glasgow mathematical journal, Tome 55 (2013) no. 1, pp. 69-83

Voir la notice de l'article provenant de la source Cambridge University Press

We give a complete description of bounded composition operators on model subspaces KB, where B is a finite Blaschke product. In particular, if B has at least one finite pole, we show that the collection of all bounded composition operators on KB has a group structure. Moreover, if B has at least two distinct finite poles, this group is finite and cyclic.
DOI : 10.1017/S0017089512000341
Mots-clés : Primary: 47B33, Secondary: 30D50, 32A35
MASHREGHI, JAVAD; SHABANKHAH, MAHMOOD. COMPOSITION OPERATORS ON FINITE RANK MODEL SUBSPACES. Glasgow mathematical journal, Tome 55 (2013) no. 1, pp. 69-83. doi: 10.1017/S0017089512000341
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[1] 1.Beurling, A., On two problems concerning linear transformations in Hilbert space, Acta Math. 81 (1949), 239–255. Google Scholar | DOI

[2] 2.Chen, H. and Gauthier, P., Composition operators of μ-Bloch spaces, Canad. J. Math. 61 (2009), 50–75. Google Scholar

[3] 3.Cowen, C. C., Composition operators on H 2, J. Operator Theory 9 (1983), 77–106. Google Scholar

[4] 4.Cowen, C. C., Linear fractional composition operators on H 2, J. Integral Equ. Operator Theory 11 (1988), 151–160. Google Scholar

[5] 5.Cowen, C. and Maccluer, B. D., Composition operators on spaces of analytic functions, in Studies in Advanced Mathematics, 1st edn. (CRC Press, Boca Raton, FL, 1995), 117–221. Google Scholar

[6] 6.Frostman, O., Sur les produits de Blaschke (French), Kungl. Fysiografiska SŤ/llskapets i Lund Frhandlingar (Proc. Roy. Physiog. Soc. Lund) 12 (15) (1942), 169–182. MR 0012127 (6:262e) Google Scholar

[7] 7.Ghatage, P., Zheng, D. and Zorboska, N., Sampling sets and closed range composition operators on the Bloch space, Proc. Amer. Math. Soc. 133 (2004), 1371–1377. Google Scholar

[8] 8.Gimémez, J., Malavé, R. and Ramos Fernàndez, J. C., Composition operators on μ-Bloch type spaces, Rend. Circ. Mat. Palermo 59 (2) (2010), 107–119. Google Scholar

[9] 9.Maccluer, B., Compact composition operators in Hp(B), Michigan Math. J. 32 (1985), 237–248. Google Scholar

[10] 10.Maccluer, B. D. and Shapiro, J. H., Angular derivatives and compact composition operators on the Hardy and Bergman spaces, Canad. Math. J. 38 (1986), 878–906. Google Scholar

[11] 11.Maccluer, B. D., Zeng, X. and Zorboska, N., Composition operators on small weighted Hardy spaces, Illinois J. Math. 40 (1996), 662–667. Google Scholar

[12] 12.Needham, T., Visual complex analysis (Oxford University Press, Oxford, UK, 2002). Google Scholar

[13] 13.Shapiro, J. H., Composition operators and classical function theory, in Univeritext: Tracts in Mathematics (Springer-Verlag, 1993). Google Scholar

[14] 14.Shapiro, J. H. and Taylor, P. D., Compact, nuclear and Hilbert-Schmidt composition operators on H 2, Indiana Univ. Math. J. 23 (1973), 471–496. Google Scholar

[15] 15.Tjani, M., Compact composition operators on Besov spaces, Trans. Amer. Math. Soc. 355 (11) (2003), 4683–4698. Google Scholar

[16] 16.Wulan, H., Zheng, D. and Zhu, K., Compact composition operators on BMOA and the Bloch space, Proc. Amer. Math. Soc. 137 (2009), 3861–3868. Google Scholar

[17] 17.Zorboska, N., Composition operators on weighted Dirichlet spaces, Proc. Amer. Math. Soc. 126 (7) (1998), 2013–2023. Google Scholar | DOI

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