Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
bounded analytic function spaces; weighted composition operators; essential norm; spectra
bounded analytic function spaces; weighted composition operators; essential norm; spectra
Summary:
Let $E$ be a complex Banach space, with the unit ball $B_E$. We study the spectrum of a bounded weighted composition operator $uC_{\varphi }$ on $H^\infty (B_E)$ determined by an analytic symbol $\varphi $ with a fixed point in $B_E$ such that $\varphi (B_E)$ is a relatively compact subset of $E$, where $u$ is an analytic function on $B_E$.
References:
[1] Aron, R., Lindström, M.: Spectra of weighted composition operators on weighted Banach spaces of analytic functions. Isr. J. Math. 141 (2004), 263-276. DOI 10.1007/BF02772223 | MR 2063037
[2] Aron, R., Galindo, P., Lindström, M.: Compact homomorphisms between algebras of analytic functions. Stud. Math. 123 (1997), 235-247. MR 1441536
[3] Bonet, J., Galindo, P., Lindström, M.: Spectra and essential spectral radii of composition operators on weighted Banach spaces of analytic functions. J. Math. Anal. Appl. 340 (2008), 884-891. DOI 10.1016/j.jmaa.2007.09.006 | MR 2390895
[4] Bourdon, P., Shapiro, J.: Mean growth of Königs eigenfunctions. J. Am. Math. Soc. 10 (1997), 299-325. DOI 10.1090/S0894-0347-97-00224-5 | MR 1401457 | Zbl 0870.30018
[5] Cowen, C. C., MacCluer, B. D.: Spectra of some composition operators. J. Funct. Anal. 125 (1994), 223-251. DOI 10.1006/jfan.1994.1123 | MR 1297020 | Zbl 0814.47040
[6] Galindo, P., Miralles,, A.: Spectra of non power-compact composition operators on $H^\infty$ spaces. Integral Equations Oper. Theory 65 (2009), 211-222. DOI 10.1007/s00020-009-1715-9 | MR 2557025
[7] Galindo, P., Gamelin, T. W., Lindström, M.: Composition operators on uniform algebras, essential norms, and hyperbolically bounded sets. Trans. Am. Math. Soc. 359 (2007), 2109-2121. DOI 10.1090/S0002-9947-06-04098-0 | MR 2276672
[8] Galindo, P., Gamelin, T. W., Lindström, M.: Spectra of composition operators on algebras of analytic functions on Banach spaces. Proc. R. Soc. Edinb., Sect. A, Math. 139 (2009), 107-121. DOI 10.1017/S0308210507000819 | MR 2487035
[9] Lindström, M., Palmberg, N.: Spectra of composition operators on BMOA. Integral Equations Oper. Theory 53 (2005), 75-86. DOI 10.1007/s00020-004-1307-7 | MR 2183598
[10] Lefèvre, P.: Generalized essential norm of weighted composition operators on some uniform algebras of analytic functions. Integral Equations Oper. Theory 63 (2009), 557-569. DOI 10.1007/s00020-009-1672-3 | MR 2497450
[11] Montolío, A. M.: Algebras de funciones analíticas acotadas. Interpolación. Thesis Universitat de València València (2008).
[12] MacCluer, B., Saxe, K.: Spectra of composition operators on the Bloch and Bergman spaces. Isr. J. Math. 128 (2002), 325-354. DOI 10.1007/BF02785430 | MR 1910387 | Zbl 1024.47009
[13] Schechter, M.: On the spectra of operators on tensor products. J. Funct. Anal. 4 (1969), 95-99. DOI 10.1016/0022-1236(69)90024-X | MR 0257782 | Zbl 0183.14102
[14] Yuan, C., Zhou, Z.-H.: The essential norm and spectrum of a weighted composition operator on $H^\infty(B_N)$. Bull. Malays. Math. Sci. Soc 33 (2010), 499-511. MR 2732171
[15] Zheng, L.: The essential norms and spectra of composition operators on $H^\infty$. Pac. J. Math. 203 (2002), 503-510. DOI 10.2140/pjm.2002.203.503 | MR 1897912
[16] Zhou, Z.-H., Yuan, C.: Spectrum of compact weighted composition operators on the weighted Hardy space in the unit ball. J. Inequal. Appl. (2007), 1-8 Article ID 61313, doi:10.1155/2007/61313. DOI 10.1155/2007/61313 | MR 2366345 | Zbl 1138.47021
Search
Partner of
