Centered weighted composition operators via measure theory. (English) Zbl 1463.47083

Summary: 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.


47B33 Linear composition operators
47B20 Subnormal operators, hyponormal operators, etc.
47B38 Linear operators on function spaces (general)
Full Text: DOI


[1] Caradus, S. R., Generalized Inverses and Operator Theory, Queen’s Pap. Pure Appl. Math. 50. Queen’s University, Kingston, Ontario (1978) · Zbl 0434.47003
[2] Embry-Wardrop, M.; Lambert, A., Measurable transformations and centred composition operators, Proc. R. Ir. Acad., Sect. A 90 (1990), 165-172 · Zbl 0753.47011
[3] Embry-Wardrop, M.; Lambert, A., Subnormality for the adjoint of a composition operator on \(L^2\), J. Oper. Theory 25 (1991), 309-318 · Zbl 0795.47022
[4] Giselsson, O., Half-centered operators, Online https://arxiv.org/pdf/1602.05081v1.pdf 44 pages · Zbl 1507.47079
[5] Hoover, T.; Lambert, A.; Quinn, J., The Markov process determined by a weighted composition operator, Stud. Math. 72 (1982), 225-235 · Zbl 0503.47007 · doi:10.4064/sm-72-3-225-236
[6] Lambert, A., Hyponormal composition operators, Bull. Lond. Math. Soc. 18 (1986), 395-400 · Zbl 0624.47014 · doi:10.1112/blms/18.4.395
[7] Morrel, B. B.; Muhly, P. S., Centered operators, Studia Math. 51 (1974), 251-263 · Zbl 0258.47019 · doi:10.4064/sm-51-3-251-263
[8] Singh, R. K.; Komal, B. S., Composition operators, Bull. Aust. Math. Soc. 18 (1978), 439-446 · Zbl 0377.47029 · doi:10.1017/S0004972700008303
[9] Singh, R. K.; Manhas, J. S., Composition Operators on Function Spaces, North-Holland Mathematics Studies 179. North-Holland Publishing, Amsterdam (1993) · Zbl 0788.47021 · doi:10.1016/s0304-0208(08)x7086-0
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.