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On Linear Functionals and Summability Factors for Strong Summability

Published online by Cambridge University Press:  20 November 2018

W. Balser ,
W. B. Jurkat  and
A. Peyerimhoff
W. Balser
Affiliation:
Universität Ulrn, Ulnij Oberer Eselberg, West Germany
W. B. Jurkat
Affiliation:
Universität Ulrn, Ulnij Oberer Eselberg, West Germany
A. Peyerimhoff
Affiliation:
Syracuse University, Syracuse, New York
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Let be an infinite matrix. We call a sequence A-limitable (denoted by s ∈ (A)) if the sequence anksk exists and converges.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 5 , 01 October 1978 , pp. 983 - 996
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Borwein, D., On strong and absolute summability, Proc. Glasg. Math. Soc. 4 (1960), 122–139.Google Scholar
2. Borwein, D., Linear functionals connected with strong Cesàro summability, J. London Math. Soc. 40 (1965), 628–634.Google Scholar
3. Daniel, E. C., On the absolute Norlund summability factors of infinite series, Riv. Mat. Univ. Parma (2) 5 (1964), 219–232.Google Scholar
4. Das, G., On the absolute Nôrlund summability factors of infinite series, J. London Math. Soc. 41 (1966), 685–692.Google Scholar
5. Hardy, G. H., Divergent series (Oxford 1949).Google Scholar
6. Irwin, R. L., Absolute summability factors I, Tohoku Math. J. 18 (1966), 247–254.Google Scholar
7. Irwin, R. L. and Peyerimhoff, A., On absolute summability factors, L'Enseignement mathématique 15 (1969), 159–167.Google Scholar
8. Jakimovski, A. and Russell, D. C., Best order conditions in linear spaces, with applications to limitation, inclusion, and high indices theorems for ordinary and absolute Riesz means, Stud. Math. 56 (1976), 101–120.Google Scholar
9. Kogbetliantz, E., Sur les séries absolument sommables par la méthode des moyennes arithmétiques, Bull. Sci. Math. (2) 49 (1925), 234–256.Google Scholar
10. Lai, S. N., On the absolute harmonie summability of the factored power series on its circle of convergence, Indian J. Math. 5 (1963), 55–66.Google Scholar
11. Lorentz, G. G. and Zeller, K., Strong and ordinary summability, Tohoku Math. J. 15 (1963), 315–321.Google Scholar
12. Moore, C. N., Summable series and convergence factors, Amer. Math. Soc. Coll. Publ. 22 (1938).Google Scholar
13. Pati, T., The summability factors of infinite series, Duke Math. J. 21 (1954), 271–284.Google Scholar
14. Pati, T., Absolute Cesàro summability factors of infinite series, Math. Zeitschr. 78 (1962), 293–297.Google Scholar
15. Peyerimhoff, A., Lectures on summability, Lecture Notes Series (S. Springer, Berlin, Heidelberg, New York, 1966).Google Scholar
16. Peyerimhoff, A., Uber einen Satz von Herrn Kogbetliantz aus der Théorie der absoluten Cesâroschen Summierbarktie, Arch. Math. 3 (1952), 262–265.Google Scholar
17. Zeller, K., Allgemeine Eigenschaften von Limitierungsverfahren, Math. Zeitschr. 53 (1951), 463–487.Google Scholar
18. Zeller, K., Théorie der Limitierungsverfahren (S. Springer, Berlin Heidelberg New York, 1970).Google Scholar