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Lindström, Mikael; Sanatpour, Amir H.

Derivative-free characterizations of compact generalized composition operators between Zygmund type spaces. (English) Zbl 1188.47025

Bull. Aust. Math. Soc. 81, No. 3, 398-408 (2010).
Summary: We give derivative-free characterizations for bounded and compact generalized composition operators between (little) Zygmund type spaces. To obtain these results, we extend M.Pavlović’s corresponding result for bounded composition operators between analytic Lipschitz spaces [Math.Z.258, No.1, 81–86 (2008; Zbl 1124.47017)].

Cited in 5 Documents

MSC:

47B38 Linear operators on function spaces (general)
47B33 Linear composition operators
30H99 Spaces and algebras of analytic functions of one complex variable
46E15 Banach spaces of continuous, differentiable or analytic functions

Keywords:

Zygmund spaces; Lipschitz spaces; weighted composition operators; generalized composition operators

Citations:

Zbl 1124.47017
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Full Text: DOI

References:

[1] DOI: 10.2307/2154848 · Zbl 0826.47023 · doi:10.2307/2154848
[2] DOI: 10.2140/pjm.1999.188.339 · Zbl 0932.30034 · doi:10.2140/pjm.1999.188.339
[3] Lusky, J. Lond. Math. Soc. 51 pp 309– (1995) · Zbl 0823.46025 · doi:10.1112/jlms/51.2.309
[4] DOI: 10.1016/j.jmaa.2007.06.013 · Zbl 1135.47021 · doi:10.1016/j.jmaa.2007.06.013
[5] DOI: 10.1007/BF02392692 · Zbl 0898.30040 · doi:10.1007/BF02392692
[6] Zhu, Spaces of Holomorphic Functions in the Unit Ball (2005) · Zbl 1067.32005
[7] Duren, Theory of (1970)
[8] Rudin, Function Theory in the Unit Ball of (1980) · Zbl 0495.32001 · doi:10.1007/978-1-4613-8098-6
[9] DOI: 10.1007/s00020-006-1420-x · Zbl 1114.47028 · doi:10.1007/s00020-006-1420-x
[10] DOI: 10.1216/RMJ-1980-10-2-371 · Zbl 0433.46023 · doi:10.1216/RMJ-1980-10-2-371
[11] DOI: 10.1017/S1446788700001336 · doi:10.1017/S1446788700001336
[12] DOI: 10.1007/s00209-007-0158-8 · Zbl 1124.47017 · doi:10.1007/s00209-007-0158-8
[13] Bierstedt, Studia Math. 127 pp 137– (1998)
[14] DOI: 10.1007/BF02392949 · Zbl 0989.46011 · doi:10.1007/BF02392949
[15] DOI: 10.1216/rmjm/1181069993 · Zbl 1042.47018 · doi:10.1216/rmjm/1181069993
[16] DOI: 10.1112/S0024610700008875 · Zbl 0959.47016 · doi:10.1112/S0024610700008875
[17] DOI: 10.2307/2159930 · Zbl 0793.47037 · doi:10.2307/2159930
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