By Chad Duna, Matthew Gagne, Caixing Gu, and Jonathan E. Shapiro
This paper appears in the Journal of Mathematical Analysis and Applications, (2013).
We examine the Toeplitzness of products of composition operators and their adjoints. We show, among other things, that the adjoint of C_phi times C_phi is strongly asymptotically Toeplitz for all analytic self-maps phi of the unit disk, and that C_phi times its adjoint is Toeplitz if and only if phi is the identity or a rotation. Also, we see that C_phi times its adjoint can exhibit varying degrees of asymptotic Toeplitzness.
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