Essential spectra of weighted composition operators with hyperbolic symbols
Olli Hyvärinen ; Ilmari Nieminen
Concrete Operators, Tome 2 (2015), / Harvested from The Polish Digital Mathematics Library
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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

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:271776 
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     author = {Olli Hyv\"arinen and Ilmari Nieminen},
     title = {Essential spectra of weighted composition operators with hyperbolic symbols},
     journal = {Concrete Operators},
     volume = {2},
     year = {2015},
     zbl = {1321.47061},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_conop-2015-0006}
}

Olli Hyvärinen; Ilmari Nieminen. Essential spectra of weighted composition operators with hyperbolic symbols. Concrete Operators, Tome 2 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_conop-2015-0006/

[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. | Zbl 0801.46021

[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. | Zbl 1075.47506

[4] P. Bourdon, Spectra of some composition operators and associated weighted composition operators, J. Operator Theory 67 (2012), 537–560. | Zbl 1262.47036

[5] P. Bourdon, Spectra of composition operators with symbols in S(2), arXiv:1401.2680 [math.FA] | Zbl 04.0324.01

[6] C. Cowen, Composition operators on H2, J. Operator Theory 9 (1983), 77–106. | Zbl 0504.47032

[7] C. Cowen, B. MacCluer, Composition operators on spaces of analytic functions, CRC Press, Boca Raton, 1995. | Zbl 0873.47017

[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. | Zbl 1060.30045

[10] P.L. Duren, Theory of Hp spaces, Academic Press, 1970. | Zbl 0215.20203

[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. | Zbl 1218.47037

[13] H. Hedenmalm, B. Korenblum, K. Zhu, Theory of Bergman spaces, Springer, 2000. | Zbl 0955.32003

[14] O. Hyvärinen, M. Lindström, I. Nieminen, E. Saukko, Spectra of weighted composition operators with automorphic symbols, J. Funct. Anal. 265 (2013), 1749–1777. | Zbl 1325.47054

[15] H. Kamowitz, The spectra of a class of operators on the disc algebra, Indiana Univ. Math. J. 27 (1978), 581–610. | Zbl 0385.47016

[16] M. Möller, On the essential spectrum of a class of operators in Hilbert space, Math. Nachr. 194 (1998), 185–196. | Zbl 0919.47004

[17] V. Müller, Spectral theory of linear operators, Birkhäuser, 2003. | Zbl 1017.47001

[18] J.H. Shapiro, Composition operators and classical function theory, Springer, 1993. | Zbl 0791.30033