Every composition operator is (mean) asymptotically Toeplitz |
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| Authors: | Joel H. Shapiro |
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| Affiliation: | Department of Mathematics and Statistics, Portland State University, Portland, OR 97207, USA |
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| Abstract: | Nazarov and Shapiro recently 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 Cesàro (C,α) sense (α>0), then every composition operator on H2 becomes asymptotically Toeplitz. |
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| Keywords: | Composition operator Toeplitz operator Regular summation method |
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