Intertwining properties of bounded linear operators on the Bergman space

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.

Full Text

Article Information

Title	Intertwining properties of bounded linear operators on the Bergman space
Source	Methods Funct. Anal. Topology, Vol. 18 (2012), no. 3, 230-242
MathSciNet	MR3051793
zbMATH	1258.47039
Copyright	The 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},
}