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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
MathSciNet review: 1050017
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Abstract: We show that for a class of operators which properly contains the normal operators on ${L_2}$, \[ \frac {1}{n}\sum \limits _{i = 0}^{n - 1} {{T^i}f \to a.e.} {\text {iff}}\frac {1}{{{2^n}}}\sum \limits _{i = 0}^{{2^n} - 1} {{T^i}f \to a.e.} \] 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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Keywords: Spectral measure, normal operators, pointwise ergodic theorem
Article copyright: © Copyright 1991 American Mathematical Society