Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 9 (2014), 139 -- 147

TOEPLITZ OPERATORS AND MULTIPLICATION OPERATORS IN THE COMMUTANT OF A COMPOSITION OPERATOR ON WEIGHTED BERGMAN SPACES

Mahmood Haji Shaabani and Bahram Khani Robati

Abstract. Let φ be an analytic self-map of D. We investigate which Toeplitz operators and multiplication operators commute with a given composition operator Cφ on Apα(D) for 1 φ. We show that under a certain condition on S, S is a polynomial in Cφ.

2010 Mathematics Subject Classification: 47B33; 47B38.
Keywords: Toeplitz operator; Weighted Bergman spaces; Composition operator; Commutant; Multiplication operators.

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M. Haji Shaabani B. Khani Robati
Shiraz University of Technology Shiraz University
Department of Mathematics, Department of Mathematics, College of Sciences,
Shiraz University of Technology, Shiraz University,
Shiraz 71555-313, IRAN. Shiraz 71454, IRAN.
E-mail: shaabani@sutech.ac.ir E-mail: bkhani@shirazu.ac.ir

http://www.utgjiu.ro/math/sma