Adjoints of rationally induced composition operators

Paul S. Bourdon and Joel H. Shapiro

Journal of Functional Analysis 255 (2008), 1995-2012


Abstract: We give an elementary proof of a formula recently obtained by Hammond, Moorhouse, and Robbins for the adjoint of a rationally induced composition operator on the Hardy space H^2 [Adjoints of composition operators with rational symbol, J. Math. Anal. Appl., 341 (2008), 626-639]. We discuss some variants and implications of this formula, and use it to provide a sufficient condition for a rationally induced composition operator adjoint to be a compact perturbation of a weighted composition operator. 

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