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Differences of weighted composition operators

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Abstract

We consider differences of weighted composition operators between given weighted Bergman spaces Hν of infinite order and characterize boundedness and the essential norm of these differences.

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References

  1. J.M. Anderson and J. Duncan, Duals of Banach spaces of entire functions,Glasgow Math. J. 32 (1990), 215–220.

    Article  MATH  MathSciNet  Google Scholar 

  2. K.D. Bierstedt and W.H. Summers, Biduals of weighted Banach spaces of analytic functions,J. Austral. Math. Soc. Ser. A 54 (1993), 70–79.

    Article  MATH  MathSciNet  Google Scholar 

  3. K.D. Bierstedt, J. Bonet, and J. Taskinen, Associated weights and spaces of holomorphic functions,Studia Math. 127 (1998), 137–168.

    MATH  MathSciNet  Google Scholar 

  4. J. Bonet, P. Domański, and M. Lindström, Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic functions,Canad. Math. Bull. 42, (1999), 139–148.

    MATH  MathSciNet  Google Scholar 

  5. J. Bonet, P. Domański, M. Lindström, and J. Taskinen, Composition operators between weighted Banach spaces of analytic functions,J. Austral. Math. Soc. Ser. A 64 (1998), 101–118.

    Article  MATH  MathSciNet  Google Scholar 

  6. J. Bonet, M. Lindström, and E. Wolf, Differences of composition operators between weighted Banach spaces of holomorphic functions,J. Austral. Math. Soc. to appear.

  7. M.D. Contreras and A.G. Hernández-Díaz, Weighted composition operators in weighted Banach spaces of analytic functions,J. Austral. Math. Soc. Ser. A 69 (2000), 41–60.

    Article  MATH  MathSciNet  Google Scholar 

  8. C.C. Cowen and B.D. MacCluer,Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1995.

    MATH  Google Scholar 

  9. A. Galbis, Weighted Banach spaces of entire functions,Arch. Math. (Basel) 62 (1994), 58–64.

    MATH  MathSciNet  Google Scholar 

  10. T. Hosokawa, K. Izuchi, and D. Zheng, Isolated points and essential components of composition operators onH ,Proc. Amer. Math. Soc. 130 (2002), 1765–1773.

    Article  MATH  MathSciNet  Google Scholar 

  11. W. Kaballo, Lifting-Probleme fürH -Funktionen,Arch. Math. (Basel) 34 (1980), 540–549.

    MATH  MathSciNet  Google Scholar 

  12. M. Lindström and E. Wolf, Essential norm of differences of weighted composition operators,Monatsh. Math. 153 (2008), 133–143.

    Article  MATH  MathSciNet  Google Scholar 

  13. W. Lusky, On the structure of o (D),Math. Nachr. 159 (1992), 279–289.

    Article  MATH  MathSciNet  Google Scholar 

  14. W. Lusky, On weighted spaces of harmonic and holomorphic functions,J. London Math. Soc. (2)51 (1995), 309–320.

    MATH  MathSciNet  Google Scholar 

  15. B. MacCluer, S. Ohno, and R. Zhao, Topological structure of the space of compositon operators onH ,Integral Equations Operator Theory 40 (2001), 481–494.

    Article  MATH  MathSciNet  Google Scholar 

  16. A. Montes-Rodríguez, Weighted composition operators on weighted Banach spaces of analytic funtions,J. London Math. Soc. (2)61 (2000), 872–884.

    Article  MATH  MathSciNet  Google Scholar 

  17. P. Nieminen, Compact differences of composition operators on Bloch and Lipschitz spaces,Comput. Methods Funct. Theory 7 (2007), 325–344.

    MATH  MathSciNet  Google Scholar 

  18. L.A. Rubel and A.L. Shields, The second duals of certain spaces of analytic functions,J. Austral. Math. Soc. 11 (1970), 276–280.

    Article  MATH  MathSciNet  Google Scholar 

  19. J.H. Shapiro,Composition Operators and Classical Function Theory, SpringerVerlag, New York, 1993.

    MATH  Google Scholar 

  20. A.L. Shields and D.L. Williams, Bounded projections, duality, and multipliers in spaces of harmonic functions,J. Reine Angew. Math. 299/300 (1978), 256–279.

    MathSciNet  Google Scholar 

  21. A.L. Shields and D.L. Williams, Bounded projections and the growth of harmonic conjugates in the disc,Michigan Math. J. 29 (1982), 3–25.

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Elke Wolf.

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Wolf, E. Differences of weighted composition operators. Collect. Math. 60, 1–10 (2009). https://doi.org/10.1007/BF03191212

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  • DOI: https://doi.org/10.1007/BF03191212

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