On Invertible Weighted Composition Operator on Hardy Space H^2
Abstract
In this paper we study the product of a weighted composition operator 𝒲𝑓,𝜑 with the adjoint of a weighted composition operator 𝒲𝑓,𝜓 ∗ on the Hardy space ℍ2 . The order of the product give rise to different cases . We will try to completely describe when the operator 𝒲𝑓,𝜑𝒲𝑓,𝜓 ∗ is invertible, isometric and unitary and when the operator 𝒲𝑓,𝜓 ∗ 𝒲𝑓,𝜑 is isometric and unitary.
Downloads
References
Abood E.H., " The composition operator on Hardy space H^2", Ph.D. Thesis, University of Baghdad, (2003).
Berberian, S.K., Introduction to Hilbert Space, Sec. Ed., Chelesa publishing Com., New York, N.Y., 1976.
CowenC. C. and Ko E.,"Hermitian weighted composition operator on H^2 "Trans.Amer.Math.Soc., 362(2010), 5771-5801.
Deddnes J. A. , "Analytic Toeplitz and Composition Operators", Con. J. Math., vol(5), 859-865, (1972).
GunatillakeG.,"invertible weighted composition operator ",J. Funct. Anal., 261(2011), 831-860.
Halmos P. R.,"A Hilbert space problem book", Sprinrer- Verlag, NewYork,(1974).
Nordgren, E. A., Composition operator, Can. J. Math. 20(1968), 442-449.
Shapiro J.H., "Composition Operators and Classical Function Theory", Springer- Verlage,New York, (1993).
Clifford, J. H. , Le, T. and Wiggins, A. ,Invertible composition operators : The product of a composition operators with adjoint of a composition operators,
Akeroyd, J. R. and Ghatage, P. G.,Closed range composition operators on A^2, Illinois J. Math. 52 (2008) ,533-549 .
Copyright (c) 2016 Journal of Progressive Research in Mathematics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
