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Individual ergodic theorem for normal operators in \(L_ 2\). (English) Zbl 0479.47005


MSC:

47A35 Ergodic theory of linear operators
47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)

Citations:

Zbl 0457.47012
Full Text: DOI

References:

[1] N. Dunford and J. T. Schwartz, Linear Operators, Vols. I and II, Wiley, New York?London (1958, 1963). · Zbl 0084.10402
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[3] D. Burkholder, ”Semi-Gaussian subspaces,” Trans. Am. Math. Soc.,104, No. 1, 123-161 (1962). · Zbl 0131.35001 · doi:10.1090/S0002-9947-1962-0138986-6
[4] V. F. Gaposhkin (Gaposkin), ”Criteria for the strong law of large numbers for some classes of second-order stationary processes and homogeneous random fields,” Teor. Veroyatn. Ee Primen.,22, No. 2, 295-319 (1977).
[5] V. F. Gaposhkin (Gaposkin), ”A theorem on the convergence almost everywhere of a sequence of measurable functions, and its applications to sequences of stochastic integrals,” Mat. Sb.,104 (16), 3-21 (1977) [MATH. USSR Sb.,33, 1 (1977)].
[6] R. Duncan, ”Pointwise convergence theorems for self-adjoint and unitary contractions,” Ann. Probab.,5, No. 4, 622-626 (1977). · Zbl 0368.40001 · doi:10.1214/aop/1176995773
[7] D. Burkholder and Y. Chen, ”Iterates of conditional expectation operators,” Proc. Am. Math. Soc.,12, No. 3, 490-495 (1961). · Zbl 0106.33201 · doi:10.1090/S0002-9939-1961-0142144-3
[8] E. Hille and R. S. Phillips, Functional Analysis and Semigroups, Am. Math. Soc. Coll. Publ.,31 (1957). · Zbl 0078.10004
[9] V. F. Gaposhkin (Gaposkin), ”The local ergodic theorem for groups of unitary operators and second-order stationary processes,” Mat. Sb.,111, 249-265 (1980).
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