Intertwining relations and extended eigenvalues for analytic Toeplitz operators

Paul S. Bourdon and Joel H. Shapiro


 Illinois J. Math. 52 (2008) 1007--1030

Abstract: We study the intertwining relation XTf = TgX, where Tf and Tg are the Toeplitz operators induced on the Hardy space H2 by analytic functions f and g that are bounded on the open unit disc U. Our work centers on the connection between intertwining and the containment of the image of g in the image of f, as well as on the nature of the intertwining operator X. We use our results to study the "extended eigenvalues" of analytic Toeplitz operators.

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