In this paperwe study both the spectra and the essential spectra ofweighted composition operators on Hardy spaces Hp(ⅅ), standard weighted Bergman spaces Apα(ⅅ) and weighted H∞1-type spaces when the symbols are of hyperbolic type
Department of Mathematical Sciences, P.O. Box 3000, 90014 University of Oulu, Finland
Bibliografia
[1] Y.A. Abramovich, C.D. Aliprantis, An invitation to operator theory, Graduate Studies inMathematics, Vol. 50, AmericanMathematical Society, Rhode Island, 2002.
[2] K. Bierstedt, W. Summers, Biduals of weighted Banach spaces of analytic functions, J. Austral. Math. Soc. Ser. A 54 (1993), 70–79.
[3] J. Bonet, P. Domanski, M. Lindström, Weakly compact composition operators on analytic vector-valued function spaces, Ann. Acad. Sci. Fenn. Math. 26 (2001), 233–248.
[4] P. Bourdon, Spectra of some composition operators and associated weighted composition operators, J. Operator Theory 67 (2012), 537–560.
[5] P. Bourdon, Spectra of composition operators with symbols in S(2), arXiv:1401.2680 [math.FA]
[6] C. Cowen, Composition operators on H2, J. Operator Theory 9 (1983), 77–106.
[7] C. Cowen, B. MacCluer, Composition operators on spaces of analytic functions, CRC Press, Boca Raton, 1995.
[8] C. Cowen, E. Ko, D. Thompson, F. Tian, Spectra of some weighted composition operators on H2, arXiv:1405.5173 [math.FA]
[9] P. Domanski, M. Lindström, Sets of interpolation and sampling for weighted Banach spaces of holomorphic functions, Ann. Polon. Math. 79 (2002), 233–264.
[10] P.L. Duren, Theory of Hp spaces, Academic Press, 1970.
[11] P.L. Duren, A. Schuster, Bergman spaces,Mathematical Surveys and Monographs Vol. 100, AmericanMathematical Society, 2004.
[12] G. Gunatillake, Invertible weighted composition operators, J. Funct. Anal. 261 (2011), 831–860.
[13] H. Hedenmalm, B. Korenblum, K. Zhu, Theory of Bergman spaces, Springer, 2000.
[14] O. Hyvärinen, M. Lindström, I. Nieminen, E. Saukko, Spectra of weighted composition operators with automorphic symbols, J. Funct. Anal. 265 (2013), 1749–1777.
[15] H. Kamowitz, The spectra of a class of operators on the disc algebra, Indiana Univ. Math. J. 27 (1978), 581–610.
[16] M. Möller, On the essential spectrum of a class of operators in Hilbert space, Math. Nachr. 194 (1998), 185–196.
[17] V. Müller, Spectral theory of linear operators, Birkhäuser, 2003.
[18] J.H. Shapiro, Composition operators and classical function theory, Springer, 1993.