Mathematica Bohemica, online first, 12 pp.

Centered weighted composition operators via measure theory

Mohammad Reza Jabbarzadeh, Mehri Jafari Bakhshkandi

Received September 9, 2016.   First published May 31, 2017.

Mohammad Reza Jabbarzadeh, Mehri Jafari Bakhshkandi, Faculty of Mathematical Sciences, University of Tabriz, P. O. Box: 5166615648, Tabriz, Iran, e-mail: mjabbar@tabrizu.ac.ir, m_jafari@tabrizu.ac.ir

Abstract: We describe the centered weighted composition operators on $L^2(\Sigma)$ in terms of their defining symbols. Our characterizations extend Embry-Wardrop-Lambert's theorem on centered composition operators.

Keywords: Aluthge transform; Moore-Penrose inverse; weighted composition operator; conditional expectation; centered operator

Classification (MSC 2010): 47B20, 47B38

DOI: 10.21136/MB.2017.0080-16

Full text available as PDF.


References:
  [1] S. R. Caradus: Generalized Inverses and Operator Theory. Queen's Pap. Pure Appl. Math. 50. Queen's University, Kingston, Ontario (1978). MR 0523736 | Zbl 0434.47003
  [2] M. Embry-Wardrop, A. Lambert: Measurable transformations and centred composition operators. Proc. R. Ir. Acad., Sect. A 90 (1990), 165-172. MR 1150455 | Zbl 0753.47011
  [3] M. Embry-Wardrop, A. Lambert: Subnormality for the adjoint of a composition operator on $L^2$. J. Oper. Theory 25 (1991), 309-318. MR 1203036 | Zbl 0795.47022
  [4] O. Giselsson: Half-centered operators. Online https://arxiv.org/pdf/1602.05081v1.pdf 44 pages.
  [5] T. Hoover, A. Lambert, J. Quinn: The Markov process determined by a weighted composition operator. Stud. Math. 72 (1982), 225-235. MR 0671398 | Zbl 0503.47007
  [6] A. Lambert: Hyponormal composition operators. Bull. Lond. Math. Soc. 18 (1986), 395-400. DOI 10.1112/blms/18.4.395 | MR 0838810 | Zbl 0624.47014
  [7] B. B. Morrel, P. S. Muhly: Centered operators. Studia Math. 51 (1974), 251-263. MR 0355658 | Zbl 0258.47019
  [8] R. K. Singh, B. S. Komal: Composition operators. Bull. Aust. Math. Soc. 18 (1978), 439-446. DOI 10.1017/S0004972700008303 | MR 0508815 | Zbl 0377.47029
  [9] R. K. Singh, J. S. Manhas: Composition Operators on Function Spaces. North-Holland Mathematics Studies 179. North-Holland Publishing, Amsterdam (1993). DOI 10.1016/s0304-0208(08)x7086-0 | MR 1246562 | Zbl 0788.47021


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