Abstract
The theorem of Steinitz on the form of the set of points which are sums of convergent rearrangements of a given series is extended to series Σxk in the uniformly smooth Banach space X with modulus of smoothness ρ(t), satisfying the condition Σρ(¦|xk¦|) < ∞.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
V. Drobot, “Rearrangements of series of functions,” Trans. Amer. Math. Soc.,142, 239–248 (1969).
J. Lindenstrauss, “On the modulus of smoothness and divergent series in Banach spaces,” Michigan Math. J.,10, No. 3, 241–252 (1963).
S. Troyanski, “On conditional convergence of series in certain F-spaces,” Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, Khar'kov, No. 5, 102–107 (1967).
M. I. Kadets, “On conditional convergence of series in Lp spaces,” Uspekhi Matem. Nauk,9, No. 1 (59), 107–109 (1954).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 11, No. 2, pp. 209–214, February, 1972.
In conclusion, the author expresses deep gratitude to M. I. Kadets for the formulation of the problem and guidance in the solution.
Rights and permissions
About this article
Cite this article
Fonf, V.P. Conditionally convergent series in a uniformly smooth Banach space. Mathematical Notes of the Academy of Sciences of the USSR 11, 129–132 (1972). https://doi.org/10.1007/BF01097931
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01097931