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McArthur, Charles W.

A note on subseries convergence. (English) Zbl 0099.27702

Proc. Am. Math. Soc. 12, 540-545 (1961).
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Cited in 5 Documents

Keywords:

series, summability
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References:

[1] A. Alexiewicz, On sequences of operations. I, Studia Math. 11 (1949), 1 – 30. · Zbl 0039.12001
[2] S. Banach, Théorie des opérations linéaires, Warsaw, Monogr. mat. vol. 1, 1932. · JFM 58.0420.01
[3] C. Bessaga and A. Pełczyński, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), 151 – 164. · Zbl 0084.09805
[4] L. W. Cohen and Nelson Dunford, Transformations on sequence spaces, Duke Math. J. 3 (1937), no. 4, 689 – 701. · Zbl 0018.07101 · doi:10.1215/S0012-7094-37-00357-0
[5] Mahlon M. Day, Normed linear spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge. Heft 21. Reihe: Reelle Funktionen, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1958. · Zbl 0082.10603
[6] Nelson Dunford, Uniformity in linear spaces, Trans. Amer. Math. Soc. 44 (1938), no. 2, 305 – 356. · Zbl 0019.41604
[7] Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London, 1958. · Zbl 0084.10402
[8] I. M. Gelfand, Abstrakte Funktionen und lineare Operatoren, Mat. Sb. (N. S.) (4) vol. 46 (1938) pp. 235-286. · JFM 64.0368.02
[9] T. H. Hildebrandt, On unconditional convergence in normed vector spaces, Bull. Amer. Math. Soc. 46 (1940), 959 – 962. · Zbl 0024.41202
[10] Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, Providence, R. I., 1957. rev. ed. · Zbl 0078.10004
[11] W. Orlicz, Beiträge zur Theorie der Orthogonalentwicklungen. II, Studia Math. vol. 1 (1929) pp. 241-255. · JFM 55.0164.02
[12] B. J. Pettis, On integration in vector spaces, Trans. Amer. Math. Soc. 44 (1938), no. 2, 277 – 304. · Zbl 0019.41603
[13] R. S. Phillips, On linear transformations, Trans. Amer. Math. Soc. 48 (1940), 516 – 541. · Zbl 0025.34202
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