Every composition operator is
(mean) asymptotically Toeplitz


Joel Shapiro


J. Math. Anal. Appl. 333 (2007), 523--529.
Abstract: Recently Fedor Nazarov and I showed that, while composition operators on the Hardy space H2 can only trivially be Toeplitz, or even  ``Toeplitz plus compact,''  it is an interesting problem to determine which of them can be ``asymptotically Toeplitz.'' I show here that if ``asymptotically'' is interpreted in, for example, the sense of Cesaro convergence, then every composition operator on H2 becomes asymptotically Toeplitz.


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