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THE WINTNER THEOREM IN UNITAL COMPLETE RANDOM NORMED ALGEBRAS

  • Tang, Yuehan (College of Mathematics Physics and Information Engineering Jiaxing University)
  • Received : 2012.07.27
  • Published : 2013.11.30

Abstract

The main purpose of this paper is to give the Wintner theorem in unital complete random normed algebras which is a random generalization of the classical Wintner theorem in Banach algebras. As an application of the Wintner theorem in unital complete random normed algebras, we also obtain that the identity operator on a complete random normed module is not a commutator.

Keywords

References

  1. N. Dunford and J. T. Schwartz, Linear Operators, Part I, Interscience, New York, 1957.
  2. T. X. Guo, Extension theorems of continuous random linear operators on random domains, J. Math. Anal. Appl. 193 (1995), no. 1, 15-27. https://doi.org/10.1006/jmaa.1995.1221
  3. T. X. Guo, The Radon-Nikodym property of conjugate spaces and the w*-equivalence the-orem for w*-measurable functions, Sci. China Ser. A 39 (1996), 1034-1041.
  4. T. X. Guo, Module homomorphisms on random normed modules, Northeast. Math. J. 12 (1996), no. 1, 102-114.
  5. T. X. Guo, A characterization for a complete random normed module to be random reflexive, J. Xiamen Univ. Natur. Sci. 36 (1997), 499-502.
  6. T. X. Guo, Some basic theories of random normed linear spaces and random inner product spaces, Acta Anal. Funct. Appl. 1 (1999), no. 2, 160-184.
  7. T. X. Guo, Representation theorems of the dual of Lebesgue-Bochner function spaces, Sci. China Ser. A 43 (2000), no. 3, 234-243. https://doi.org/10.1007/BF02897846
  8. T. X. Guo, Several applications of the theory of random conjugate spaces to measurability problems, Sci. China Ser. A 50 (2007), no. 5, 737-747.
  9. T. X. Guo, Relations between some basic results derived from two kinds of topologies for a random locally convex module, J. Funct. Anal. 258 (2010), no. 9, 3024-3047. https://doi.org/10.1016/j.jfa.2010.02.002
  10. T. X. Guo, Recent progress in random metric theory and its applications to conditional risk measures, Sci. China Ser. A 54 (2011), no. 4, 633-660. https://doi.org/10.1007/s11425-011-4189-6
  11. T. X. Guo and S. B. Li, The James theorem in complete random normed modules, J. Math. Anal. Appl. 308 (2005), no. 1, 257-265. https://doi.org/10.1016/j.jmaa.2005.01.024
  12. T. X. Guo and Z. Y. You, A Riesz representation theorem for random inner product modules and its applications, Chinese Ann. Math. Ser. A 17 (1996), no. 3, 361-364.
  13. T. X. Guo and Z. Y. You, A note on pointwise best approximation, J. Approx. Theory 93 (1998), no. 2, 344-347. https://doi.org/10.1006/jath.1997.3173
  14. C. E. Rickart, General Theory of Banach Algebras, D. Van Nostrand Company, Inc., 1960.
  15. Y. H. Tang, A new version of the Gleason-Kahane-Zelazko theorem in complete random normed algebras, J. Inequal. Appl. 2012 (2012), 6 pp. https://doi.org/10.1186/1029-242X-2012-6
  16. Y. H. Tang, Random spectral theorems of self-adjoint random linear operators on complete complex random inner product modules, Linear Multilinear Algebra 61 (2013), no. 3, 409-416. https://doi.org/10.1080/03081087.2012.689981
  17. Y. H. Tang and T. X. Guo, Complete random normed algebras, in press.
  18. G. Weiss, B(H)-commutators: A historical survey, operator theory, Advances and Applications 153 (2004), 307-320.
  19. A.Wintner, The unboundedness of quantum-mechanical matrices, Phys. Rev. 71 (1947), 738-739.

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