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Proceedings of the American Mathematical Society

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Rearrangements of conditionally convergent real series with preassigned cycle type


Author: John Howard Smith
Journal: Proc. Amer. Math. Soc. 47 (1975), 167-170
DOI: https://doi.org/10.1090/S0002-9939-1975-0352772-8
MathSciNet review: 0352772
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Abstract | References | Additional Information

Abstract: For any conditionally convergent real series, any real number $ r$, and any infinite cycle type, there is a permutation of the indices, of the given cycle type, which makes the series converge to $ r$.


References [Enhancements On Off] (What's this?)

  • [1] R. P. Agnew, Permutations preserving convergence of series, Proc. Amer. Math. Soc. 6 (1955), 563-564. MR 17, 146. MR 0071559 (17:146g)
  • [2] P. R. Halmos, Permutations of sequences and the Schröder-Bernstein theorem, Proc. Amer. Math. Soc. 19 (1968), 509-510. MR 37 #2179. MR 0226590 (37:2179)
  • [3] J. von Neumann, Characterisierung des Spektrums eines Integraloperators, Actualités Sci. Indust., no. 229, Hermann, Paris, 1935, pp. 11-12.
  • [4] E. Steinitz, Bedingt konvergente Reihen und konvexe systeme, J. Reine Angew. Math. 143 (1913), 128-175; ibid. 144 (1914), 1-40; 146 (1916), 1-52.


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0352772-8
Keywords: Conditionally convergent series, cycle type of permutation
Article copyright: © Copyright 1975 American Mathematical Society

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