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Pseudospectral operators and the pointwise ergodic theorem


Author: R. E. Bradley
Journal: Proc. Amer. Math. Soc. 112 (1991), 863-870
MSC: Primary 47A35; Secondary 28D05, 47B15
DOI: https://doi.org/10.1090/S0002-9939-1991-1050017-6
MathSciNet review: 1050017
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that for a class of operators which properly contains the normal operators on $ {L_2}$,

$\displaystyle \frac{1}{n}\sum\limits_{i = 0}^{n - 1} {{T^i}f \to a.e.} {\text{iff}}\frac{1}{{{2^n}}}\sum\limits_{i = 0}^{{2^n} - 1} {{T^i}f \to a.e.} $

This theorem is used to give an alternate form of a theorem of Gaposhkin concerning the pointwise ergodic theorem for normal operators.

References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1050017-6
Keywords: Spectral measure, normal operators, pointwise ergodic theorem
Article copyright: © Copyright 1991 American Mathematical Society

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