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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Equicontinuity, affine mean ergodic theorem and linear equations in random normed spaces
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by V. Radu PDF
Proc. Amer. Math. Soc. 57 (1976), 299-303 Request permission

Abstract:

The aim of this paper is to give a characterization of equicontinuous families of linear operators in random normed spaces which generalizes the normed spaces case. This characterization is used to generalize some results on iterative solutions of linear equations by using the affine mean ergodic theorem for locally convex spaces (note that every Fr 'echet space is a random normed space with the $t$-norm $T = {\text {Min}}$).
References
  • W. G. Dotson Jr., Mean ergodic theorems and iterative solution of linear functional equations, J. Math. Anal. Appl. 34 (1971), 141–150. MR 301529, DOI 10.1016/0022-247X(71)90164-8
  • Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
    • V. I. IstrÇŽĹŁescu, Introducere Ă®n teoria spaĹŁiilor metrice probabiliste Ĺźi aplicaĹŁii, Editura TehnicÇŽ, BucureĹźti, 1974.
  • Karl Menger, Statistical metrics, Proc. Nat. Acad. Sci. U.S.A. 28 (1942), 535–537. MR 7576, DOI 10.1073/pnas.28.12.535
  • D. H. Muštari, The linearity of isometric mappings of random normed spaces, Kazan. Gos. Univ. UÄŤen. Zap. 128 (1968), no. 2, 86–90 (Russian). MR 0487377
  • Octav Onicescu, Nombres et systèmes alĂ©atoires, Éditions de l’AcadĂ©mie de la RĂ©publique Populaire Roumaine, Bucharest; Éditions Eyrolles, Paris, 1964 (French). MR 0172314
  • V. Radu, Linear operators in random normed spaces, Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.) 17(65) (1973), 217–220 (1975). MR 365650
    • —, On a random norm and continuity of linear operators on random normed spaces, C. R. Acad. Sci. Paris 280 (1975), 1303-1305. B. Schweizer, Lectures on $P$. $M$-spaces, Lectures Notes, the University of Arizona, 1965 (unpublished).
  • B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. Math. 10 (1960), 313–334. MR 115153
    • A. N. Ĺ erstnev, The notion of random normed space, Dokl. Akad. Nauk SSSR 149 (1963), 280-283 = Soviet Math. Dokl. 4 (1963), 388-391. MR 27 #4268.
  • A. N. Ĺ erstnev, Random normed spaces. Questions of completeness, Kazan. Gos. Univ. UÄŤen. Zap. 122 (1962), no. kn. 4, 3–20 (Russian). MR 0174032
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 57 (1976), 299-303
  • MSC: Primary 47A50; Secondary 46A15, 47A35
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0473883-3
  • MathSciNet review: 0473883