Abstract
The spectra and essential spectra of some weighted composition operators arising from non-automorphic parabolic self-maps of the unit disc acting on a class of Banach spaces- not necessarily reflexive- of analytic functions is shown to be a spiral-like set, as it happens in the cases treated earlier.
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References
Abramovich, Y.A., Aliprantis, C.D.: An Invitation to Operator Theory. AMS, Providence (2002)
Contreras, M.D., Hernandez-Díaz, A.G.: Weighted composition operators in weighted Banach spaces of analytic functions. J. Aust. Math. Soc. Ser. A 69(1), 41–60 (2000)
Cowen, C.: Composition operators in \(H^2\). J. Oper. Theory 9, 77–106 (1983)
Cowen, C., MacCluer, B.D.: Composition Operators on Spaces of Analytic Functions. CRC Press, Boca Raton (1995)
Duren, P., Gallardo-Gutiérrez, E., Montes-Rodríguez, A.: A Paley–Wiener theorem for Bergman spaces with application to invariant subspaces. Bull. Lond. Math. Soc. 39(3), 459–466 (2007)
Eklund, T., Galindo, P., Lindström, M., Nieminen, I.: Norm, essential norm and weak compactness of weighted composition operators between dual Banach spaces of analytic functions. J. Math. Anal. Appl. 451, 1–13 (2017)
Gallardo-Gutiérrez, E., Schroderus, R.: The spectra of linear fractional composition operators on weighted Dirichlet spaces. J. Funct. Anal. 271(3), 720–745 (2016)
Higdon, W.M.: The spectra of composition operators from linear fractional maps acting upon the Dirichlet space. J. Funct. Anal. 220(1), 55–75 (2005)
Hurst, P.R.: Relating composition operators on different weighted Hardy spaces. Arch. Math. (Basel) 68(6), 503–513 (1997)
MacCluer, B.D., Zeng, X., Zorboska, N.: Composition operators on small weighted Hardy spaces. Ill. J. Math. 40(4), 662–677 (1996)
Montes-Rodríguez, A.: Weighted composition operators on weighted Banach spaces of analytic functions. J. Lond. Math. Soc. (2) 61, 872–884 (2000)
Mujica, J.: Complex Analysis in Banach Spaces, vol. 120. North-Holland Mathematics Studies, Amsterdam (1986)
Ng, K.F.: On a theorem of Dixmier. Math. Scand. 29(1971), 279–280 (1972)
Pérez-González, F., Rättyä, J.: Inner functions in the Möbius invariant Besov-type spaces. Proc. Edinb. Math. Soc. (2) 52(3), 751–770 (2009)
Ransford, T.J.: The spectrum of an interpolated operator and analytic multivalued functions. Pac. J. Math. 121(2), 445–466 (1986)
Rudin, W.: Functional Analysis. International Series in Pure and Applied Mathematics, 2nd edn. McGraw-Hill, Inc., New York (1991)
Schroderus, R.: Spectra of linear fractional composition operators on the Hardy and weighted Bergman spaces of the half-plane. J. Math. Anal. Appl. 447(2), 817–833 (2017)
Shapiro, J.H.: Composition Operators and Classical Function Theory. Springer, New York (1993)
Zhu, K.: Operator Theory in Function Spaces. Marcel Dekker, New York (1990)
Zhao, R., Zhu, K.: Theory of Bergman spaces in the unit ball of \({\mathbb{C}}^n\). Mem. Soc. Math. Fr. (N.S.) 115 (2008)
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P. Galindo is partially supported by MTM2014-53241-P and M. Lindström is partially supported by MTM2014-53241-P and the Academy of Finland Project 296718.
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Galindo, P., Lindström, M. Spectra of Some Weighted Composition Operators on Dual Banach Spaces of Analytic Functions. Integr. Equ. Oper. Theory 90, 31 (2018). https://doi.org/10.1007/s00020-018-2454-6
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DOI: https://doi.org/10.1007/s00020-018-2454-6