Hostname: page-component-7479d7b7d-pfhbr Total loading time: 0 Render date: 2024-07-10T09:51:20.228Z Has data issue: false hasContentIssue false
  • English
  • Français

Some sequence spaces and almost convergence

Published online by Cambridge University Press:  09 April 2009

Sudarsan Nanda
Sudarsan Nanda
Affiliation:
Department of Mathematics, Regional Engineering College, Rourkela 769008, Orissa, India.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we investigate some new sequence spaces which naturally emerge from the concept of almost convergence. Just as ordinary, absolute and strong summability, it is expected that almost convergence must give rise to almost, absolutely almost and strongly almost summability. Almost and absolutely almost summable sequences have been discussed by several authors. The object of this paper is to introduce the spaces of strongly almost summable sequences which happen to be complete paranormed spaces under certain conditions. Some topological results, characterisation of strongly almost regular matrices, uniqueness of generalized limits and inclusion relations of such sequences have been discussed.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 22 , Issue 4 , December 1976 , pp. 446 - 455
Copyright
Copyright © Australian Mathematical Society 1976

References

Banach, S. (1932), Theorie des Operations Lineaires (Warszawa).Google Scholar
Duran, J. P. (1972), ‘Infinte matrices and almost convergence’, Math. Z. 128, 75–83.CrossRefGoogle Scholar
Das, G. and Nanda, S. (to appear), Some sequence spaces and absolute almost convergence.Google Scholar
Hamilton, H. J. and Hill, J. D. (1938), ‘On strong summability’, Amer. J. Math. 60, 588–94.CrossRefGoogle Scholar
Kuttner, B. (1946), ‘Note on strong summability’, J. London Math. Soc. 21, 118–22.Google Scholar
King, J. P. (1966), ‘Almost summable sequences’, Proc. Amer. Math. Soc. 17, 1219–25.CrossRefGoogle Scholar
Lorentz, G. G. (1948), ‘A contribution to the theory of divergent sequences’, Acta Math. 80, 167–190.CrossRefGoogle Scholar
Maddox, I. J. (1967), ‘Spaces of strongly summable sequences’, Quart. J. Math. Oxford Ser. (2) 18, 345–55.CrossRefGoogle Scholar
Maddox, I. J. and Roles, J. W. (1969), ‘Absolute convexity in certain topological linear spaces’, Proc. Camb. Philos. Soc. 66, 541–45.CrossRefGoogle Scholar
Maddox, I. J. (1970), Elements of Functional Analysis (Camb. Univ. Press).Google Scholar
Schaefer, Paul (1969), ‘Almost convergent and almost summable sequences’, Proc. Amer. Math. Soc. 20, 51–54.CrossRefGoogle Scholar