On convergence preserving transformations of infinite series. (English) Zbl 0891.40001

The paper generalizes and expands some known results concerning convergence preserving transformations of infinite series of elements of a finite-dimensional Banach space.


40A05 Convergence and divergence of series and sequences
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[1] RADO R.: A theorem of infìnite series. J. London Math. Soc. XXXV (1960), 273-276. · Zbl 0098.26703
[2] ŠALÁT T.: Infinite Series. (Slovak), Academia, Praha, 1974.
[3] SHILOV G. E.: Mathematical Analysis. Functions of a single variable. Part 3 (Russian), Nauka, Moskva, 1970. · Zbl 0314.00003
[4] SMITH A.: Convergence preserving functions: an alternative discussion. Amer. Math. Monthly 96 (1991), 831-833. · Zbl 0783.40002
[5] KUCZMA M.: An Introduction to the Theory of Functional Equations and Inequalities. PWN, Warszawa-Kraków-Katowice, 1985. · Zbl 0555.39004
[6] WILDENBERG G.: Convergence preserving functions. Amer. Math. Monthly 95 (1988), 542-544. · Zbl 0664.40001
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