Composition operators ♥ Toeplitz operators

Joel H. Shapiro

in: Five Lectures in Complex Analysis,  Contemporary Mathematics, vol. 525, Amer. Math. Soc., Providence, RI, 2010, pp. 117-139.


Abstract: The study of composition operators, most notably on the Hardy space H2, often leads to issues involving Toeplitz operators acting on that space. Toeplitz operators arise, for example, in Littlewood’s original proof that composition operators are bounded on H2, in the computation of their adjoints, and in questions about their “normality.” In addition, there are interesting questions about just how “Toeplitz” a composition operator can be. This article reviews some recent work on these matters.

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