Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-25T08:13:37.416Z Has data issue: false hasContentIssue false
  • English
  • Français

ORDER BOUNDED WEIGHTED COMPOSITION OPERATORS

Part of: Special classes of linear operators

Published online by Cambridge University Press:  09 April 2013

ELKE WOLF
ELKE WOLF*
Affiliation:
Mathematical Institute, University of Paderborn, Warburger Str. 100, 33098 Paderborn, Germany (email: [email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let $\phi $ and $\psi $ be analytic maps on the open unit disk $D$ such that $\phi (D) \subset D$. Such maps induce a weighted composition operator $C_{\phi ,\psi }$ acting on weighted Banach spaces of type $H^{\infty }$or on weighted Bergman spaces, respectively. We study when such operators are order bounded.

Keywords

weighted composition operatorsorder boundedweighted Bergman spacesweighted Banach spaces of holomorphic functions

MSC classification

Secondary: 47B33: Composition operators
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 93 , Issue 3 , December 2012 , pp. 333 - 343
Copyright
Copyright © 2013 Australian Mathematical Publishing Association Inc. 

References

[1]Anderson, J. M. and Duncan, J., ‘Duals of Banach spaces of entire functions’, Glasg. Math. J. 32 (1990), 215–220.CrossRefGoogle Scholar
[2]Bierstedt, K. D., Bonet, J. and Galbis, A., ‘Weighted spaces of holomorphic functions on balanced domains’, Michigan Math. J. 40(2) 271–297.Google Scholar
[3]Bierstedt, K. D., Bonet, J. and Taskinen, J., ‘Associated weights and spaces of holomorphic functions’, Studia Math. 127(2) (1998), 137–168.CrossRefGoogle Scholar
[4]Bierstedt, K. D., Meise, R. and Summers, W. H., ‘A projective description of weighted inductive limits’, Trans. Amer. Math. Soc. 272(1) (1982), 107–160.CrossRefGoogle Scholar
[5]Bierstedt, K. D. and Summers, W. H., ‘Biduals of weighted Banach spaces of holomorphic functions’, J. Aust. Math. Soc. Ser. A. 54 (1993), 70–79.CrossRefGoogle Scholar
[6]Cowen, C. and MacCluer, B., Composition Operators on Spaces of Analytic Functions (CRC Press, Boca Raton, FL, 1995).Google Scholar
[7]Čučković, Z. and Zhao, R., ‘Weighted composition operators on the Bergman space’, J. Lond. Math. Soc. (2) 70 (2004), 499–511.Google Scholar
[8]Domenig, T., ‘Order bounded and $p$-summing composition operators’, in: Studies on Composition Operators, Contemporary Mathematics, 213 (American Mathematical Society, Providence, RI, 1998), pp. 27–41.CrossRefGoogle Scholar
[9]Hibschweiler, R., ‘Order bounded weighted composition operators’, in: Banach Spaces of Analytic Functions, Contemporary Mathematics, 454 (American Mathematical Society, Providence, RI, 2008), pp. 93–105.CrossRefGoogle Scholar
[10]Hunziker, H., ‘Kompositionsoperatoren auf klassischen Hardyräumen’, Dissertation, Universität Zürich.Google Scholar
[11]Shapiro, J. H., Composition Operators and Classical Function Theory (Springer, New York, 1993).CrossRefGoogle Scholar
[12]Wolf, E., ‘Weighted composition operators between weighted Bergman spaces’, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 103(1) (2009), 11–15.CrossRefGoogle Scholar
[13]Wolf, E., ‘Bounded, compact and Schatten class weighted composition operators between weighted Bergman spaces’, Commun. Korean Math. Soc. 26(3) (2011), 455–462.CrossRefGoogle Scholar