×

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.

MSC:

40A05 Convergence and divergence of series and sequences
PDF BibTeX XML Cite
Full Text: EuDML

References:

[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.