Mathematica Bohemica, Vol. 143, No. 2, pp. 123-134, 2018
Centered weighted composition operators via measure theory
Mohammad Reza Jabbarzadeh, Mehri Jafari Bakhshkandi
Received September 9, 2016. First published May 31, 2017.
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.
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
Affiliations: 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
