Abstract
We prove that, in the case of double series, perfect and unconditional convergences coincide, while absolute and perfect convergences do not coincide even for numerical series.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. M. Kadets and M. I. Kadets, “Rearrangements of series in Banach spaces,” Trans. Math. Monographs, 86 (1991).
H. H. Schaefer, Topological Vector Spaces [Russian translation], Mir, Moscow (1971).
N. J. Kalton, “Spaces of compact operators,” Math. Ann., 208, 267–278 (1974).
A. Pelczynski, “Projections in certain Banach spaces,” Stud. Math, 19, 209–228 (1960).
H. P. Rosenthal, “A characterization of Banach spaces containing l 1,” Proc. Natl. Acad. Sci. USA, 71, 2411–2413 (1974).
N. Dunford and J. T. Schwartz, Linear Operators. Part I: General Theory [Russian translation], Inostrannaya Literatura, Moscow (1962).
Additional information
Kharkov Academy of Mining Industry, Kharkov. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 8, pp. 1032–1041. August, 1997.
Rights and permissions
About this article
Cite this article
Kadets, M.I. On absolute, perfect, and unconditional convergences of double series in Banach spaces. Ukr Math J 49, 1158–1168 (1997). https://doi.org/10.1007/BF02487545
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02487545