On absolute, perfect, and unconditional convergences of double series in Banach spaces
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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.
KeywordsBanach Space Compact Operator Convergent Series Converse Statement Double Series
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- 1.V. M. Kadets and M. I. Kadets, “Rearrangements of series in Banach spaces,” Trans. Math. Monographs, 86 (1991).Google Scholar
- 2.H. H. Schaefer, Topological Vector Spaces [Russian translation], Mir, Moscow (1971).Google Scholar
- 6.N. Dunford and J. T. Schwartz, Linear Operators. Part I: General Theory [Russian translation], Inostrannaya Literatura, Moscow (1962).Google Scholar
© Plenum Publishing Corporation 1998