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# 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.

### 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},
}