Geodesic
Matrix Transformations in an Incomplete Space
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 727-734

Voir la notice de l'article provenant de la source Cambridge University Press

Let X = (X, p) be a seminormed complex linear space with zero θ. Natural definitions of convergent sequence, Cauchy sequence, absolutely convergent series, etc., can be given in terms of the seminorm p. Let us write C = C(X) for the set of all convergent sequences for the set of Cauchy sequences; and L∞ for the set of all bounded sequences. 
Maddox, I. J. Matrix Transformations in an Incomplete Space. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 727-734. doi: 10.4153/CJM-1968-071-0
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[1] 1. Hardy, G. H., Divergent series (Oxford Univ. Press, Oxford, 1949). Google Scholar

[2] 2. Kothe, G. and Teoplitz, O., Lineare Rdume mit unendlich vielen Koordinaten una Ringe unendlicher Matrizen, J. Reine Angew. Math., 171 (1934), 193–226. Google Scholar

[3] 3. Lorentz, G. G. and MacPhail, M. S., Unbounded operators and a theorem of A. Robinsonf Trans. Roy. Soc. Canada, Sect. Ill, 46 (1952), 33–37. Google Scholar

[4] 4. Ramanujan, M. S., Generalised Kojima-Toeplitz matrices in certain linear topological spaces, Math. Ann., 159 (1965), 365–373. Google Scholar

[5] 5. Robinson, A., On functional transformations and summability, Proc. London Math. Soc, 52 (1950), 132–160. Google Scholar

[6] 6. Toeplitz, O., Ûber allgemeine lineare Mittelbildungen, Prace Mat. Fiz., 22 (1911), 113–119. Google Scholar

[7] 7. Wilansky, A., An application of Banach linear functional to summability, Trans. Amer. Math. Soc, 67 (1949), 59–68. Google Scholar

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