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 ,

**[A]**G. Alexits,*Problems in the convergence of orthogonal series*, Pergamon Press, New York, 1961. MR**0218827 (36:1911)****[B]**D. Burkholder,*Semi-Gaussian subspaces*, Trans. Amer. Math. Soc.**104**(1962), 123-131. MR**0138986 (25:2426)****[G1]**V. F. Gaposhkin,*A theorem on the convergence almost everywhere of a sequence of measurable functions, and its application to sequences of stochastic integrals*, Math. USSR Sbornik**33**(1977), 1-19. (English transl.)**[G2]**-,*Criteria for the strong law of large numbers for some classes of second-order stationary processes and homogeneous random fields*, Theory Probab. and Appl.**22**(1977), 286-310. (English transl.)**[G3]**-,*Individual ergodic theorem for normal operators in*, Functional Anal. Appl.**15**(1981), 14-18. (English transl.)**[H]**P. R. Halmos,*What does the spectral theorem say*? Amer. Math. Monthly**70**(1963), 241-247. MR**0150600 (27:595)**

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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