Rearrangements of conditionally convergent real series with preassigned cycle type
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- by John Howard Smith PDF
- Proc. Amer. Math. Soc. 47 (1975), 167-170 Request permission
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
- Ralph Palmer Agnew, Permutations preserving convergence of series, Proc. Amer. Math. Soc. 6 (1955), 563–564. MR 71559, DOI 10.1090/S0002-9939-1955-0071559-4
- P. R. Halmos, Permutations of sequences and the Schröder-Bernstein theorem, Proc. Amer. Math. Soc. 19 (1968), 509–510. MR 226590, DOI 10.1090/S0002-9939-1968-0226590-1 J. von Neumann, Characterisierung des Spektrums eines Integraloperators, Actualités Sci. Indust., no. 229, Hermann, Paris, 1935, pp. 11-12. 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
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 47 (1975), 167-170
- DOI: https://doi.org/10.1090/S0002-9939-1975-0352772-8
- MathSciNet review: 0352772