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Intertwining properties of bounded linear operators on the Bergman space

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Abstract

In this paper we find conditions on $\phi, \psi\in L^{\infty}(\mathbb D)$ that are necessary and sufficient for the existence of bounded linear operators $S,T$ from the Bergman space $L_a^2(\mathbb D)$ into itself such that for all $z\in \mathbb D,$ $ \phi(z)=\langle Sk_z, k_z, \rangle, \psi(z)=\langle Tk_z, k_z \rangle$ and $C_aS=TC_a$ for all $a\in \mathbb D$ where $C_af=f\circ \phi_a$ for all $f\in L_a^2(\mathbb D)$ and $\phi_a(z)=\frac{a-z}{1-\bar a z}, z\in \mathbb D.$ Applications of the results are also discussed.


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Article Information

TitleIntertwining properties of bounded linear operators on the Bergman space
SourceMethods Funct. Anal. Topology, Vol. 18 (2012), no. 3, 230-242
MathSciNet MR3051793
zbMATH 1258.47039
CopyrightThe Author(s) 2012 (CC BY-SA)

Authors Information

Namita Das P. G.
Department of Mathematics, Utkal University, Vanivihar, Bhubaneswar, 751004, Orissa, India 


Citation Example

Namita Das, Intertwining properties of bounded linear operators on the Bergman space, Methods Funct. Anal. Topology 18 (2012), no. 3, 230-242.


BibTex

@article {MFAT607,
    AUTHOR = {Das, Namita},
     TITLE = {Intertwining properties of bounded linear operators on the Bergman space},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {18},
      YEAR = {2012},
    NUMBER = {3},
     PAGES = {230-242},
      ISSN = {1029-3531},
  MRNUMBER = {MR3051793},
 ZBLNUMBER = {1258.47039},
       URL = {http://mfat.imath.kiev.ua/article/?id=607},
}


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