Every composition operator
is
(mean) asymptotically Toeplitz

Joel Shapiro

J. Math. Anal.
Appl. 333 (2007), 523529.


Abstract:
Recently Fedor Nazarov and I showed that, while composition
operators on the Hardy space H^{2} 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 H^{2} becomes asymptotically Toeplitz. 
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