Literature Cited
N. Dunford and J. T. Schwartz, Linear Operators, Vols. I and II, Wiley, New York—London (1958, 1963).
A. Blanc-Lapierre and A. Tortrat, "Sur la loi forte des grands nombres," C. R. Acad. Sci. Paris,267A, 740–743 (1968).
D. Burkholder, "Semi-Gaussian subspaces," Trans. Am. Math. Soc.,104, No. 1, 123–161 (1962).
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).
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)].
R. Duncan, "Pointwise convergence theorems for self-adjoint and unitary contractions," Ann. Probab.,5, No. 4, 622–626 (1977).
D. Burkholder and Y. Chen, "Iterates of conditional expectation operators," Proc. Am. Math. Soc.,12, No. 3, 490–495 (1961).
E. Hille and R. S. Phillips, Functional Analysis and Semigroups, Am. Math. Soc. Coll. Publ.,31 (1957).
V. F. Gaposhkin (Gaposkin), "The local ergodic theorem for groups of unitary operators and second-order stationary processes," Mat. Sb.,111, 249–265 (1980).
Additional information
Moscow Institute of Railway Transport Engineering. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 15, No. 1, pp. 18–22, January–March, 1981.
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Gaposhkin, V.F. Individual ergodic theorem for normal operators in L2 . Funct Anal Its Appl 15, 14–18 (1981). https://doi.org/10.1007/BF01082374
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DOI: https://doi.org/10.1007/BF01082374