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 ${L_2}$, \[ \frac {1}{n}\sum \limits _{i = 0}^{n - 1} {{T^i}f \to a.e.} {\text {iff}}\frac {1}{{{2^n}}}\sum \limits _{i = 0}^{{2^n} - 1} {{T^i}f \to a.e.} \] This theorem is used to give an alternate form of a theorem of Gaposhkin concerning the pointwise ergodic theorem for normal operators.

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*Semi-Gaussian subspaces*, Trans. Amer. Math. Soc.**104**(1962), 123–131. MR**138986**, DOI https://doi.org/10.1090/S0002-9947-1962-0138986-6
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Additional Information

Keywords:
Spectral measure,
normal operators,
pointwise ergodic theorem

Article copyright:
© Copyright 1991
American Mathematical Society