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Weighted composition operators on functional Hilbert spaces

Published online by Cambridge University Press:  17 April 2009

R.K. Singh  and
R. David Chandra Kumar
R.K. Singh
Affiliation:
Department of Mathematics, University of Jammu, Jammu 180001, India.
R. David Chandra Kumar
Affiliation:
Department of Mathematics, University of Jammu, Jammu 180001, India.
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Abstract

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Let X be a non-empty set and let H(X) denote a Hibert space of complex-valued functions on X. Let T be a mapping from X to X and θ a mapping from X to C such that for all f in H(X), f ° T is in H(x) and the mappings CT taking f to f ° T and M taking f to θ.f are bounded linear operators on H(X). Then the operator CTMθ is called a weighted composition operator on H(X). This note is a report on the characterization of weighted composition operators on functional Hilbert spaces and the computation of the adjoint of such operators on L2 of an atomic measure space. Also the Fredholm criteria are discussed for such classes of operators.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 31 , Issue 1 , February 1985 , pp. 117 - 126
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Abrahamse, M.B. “Multiplication operator”, Hilbert space operators, 17–36 (Lecture Notes in Mathematics, 693. Springer-Verlag, Berlin, Heidelberg, New York, 1978).Google Scholar
[2]Coughran, J.G. and Schwartz, H.J. “Spectra of composition operators”, Proc. Amer. Math. Soc. 51 (1975), 125–130.Google Scholar
[3]Nordgren, E.A. “Composition operators in Hilbert spaces”; Hilbert space operators, 37–63 (Lecture Notes in Mathematics, 693. Springer-Verlag, Berlin, Heidelberg, New York, 1978).CrossRefGoogle Scholar
[4]Singh, R.K. “Normal and Hermitian operators”, Proc. Amer. Math. Soc. 47 (1975), 348–350.Google Scholar
[5]Singh, R.K. “Invertible composition operators on L 2(λ)“, Proc. Amer. Math. Soc. 56 (1976), 127–129.Google Scholar
[6]Singh, R.K. and Komal, B.S., “Composition operator on lp and its adjoint”, Proc. Amer. Math. Soc. 70 (1978), 21–25.Google Scholar
[7]Singh, R.K. and Veluchamy, T., “Atomic measure spaces and composition operators”, Bull. Austral. Math. Soc. 27 (1983), 259–267.CrossRefGoogle Scholar
[8]Shields, A.L. and Wallen, L.J. “The commutant of certain Hubert space operators”, Indiana Univ. Math. J. 20 (1971), 777–788.CrossRefGoogle Scholar