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Toeplitz operators in the commutant of a composition operator. (English) Zbl 0924.47017

Summary: If \(\phi\) is an analytic self-mapping of the unit disc \(D\) and if \(H^2(D)\) is the Hardy-Hilbert space on \(D\), the composition operator \(C_\phi\) on \(H^2(D)\) is defined by \(C_\phi(f)= f\circ\phi\). In this article, we consider which Toeplitz operators \(T_f\) satisfy \(T_f C_\phi= C_\phi T_f\).

MSC:

47B38 Linear operators on function spaces (general)
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
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