Research Article
Year 2020,
Volume: 3 Issue: 1, 66 - 76, 31.01.2020
Abstract
In this study, we give some new FK-spaces by means of an infinite matrix as an operator and define some new beta and gama type duality of sequence spaces [3, 4]. We also introduce some new sections and investigate some properties like AB-, FAK-, SAK- and AK- in an FK-space. By this way, we obtain some new distinguished subspaces of an FK- space [5]. Among other results, we prove that the sum of infinite numbers of FK-spaces and the intersection of a sequence of FK-spaces which have these new properties with
corresponding paranorms have also these new properties. The reader can refer to [1], [2] and [11] for the main results and related topics in FK-space theory.
Keywords
References
- F. Başar, Summability Theory and Its Applications, Bentham Science Publishers, Istanbul, (2012).
- J. Boos, Classical and Modern Methods in Summability, Oxford University Press. New York, (2000).
- M. Buntinas, Convergent and bounded Cesaro sections in FK-spaces, Math. Z., Vol. 121, pp. 191-200 (1971).
- M. Buntinas, On Toeplitz sections in sequence spaces, Math. Proc. Cambridge Philos. Soc., Vol. 78, pp. 451-460 (1975).
- İ. Dağadur, On some subspaces of an FK-space, Math. Commun., Vol.7, pp. 15-20 (2002).
- R. Devos, Combinations of distinguished subsets and conullity, Math. Z., Vol. 192, pp. 447-451 (1986).
- D. J. Fleming and J. C. Magee, FK-multiplier spaces, Proc. Amer. Math. Soc., Vol. 125, N. 1, pp. 175-181 (1997).
- D. J. H. Garling, The beta and gama duality of sequence spaces, Proc. Cambridge Philos. Soc., Vol. 63, pp. 963-981 (1967).
- M. Mursaleen A. K. Noman, On the spaces of lamda convergent and bounded sequences, Thai J. Math., Vol. 8, N. 2, pp. 311-329 (2010).
- W. H. Ruckle, Sequence Spaces, Pitman Advanced Publishing Program, Boston, (1981).
- A. Wilansky, Summability Through Functional Analysis, North-Holland, Amsterdam, (1984).
- K. Zeller, Allgemeine eigenschaften von limitierungsverfahren, Math. Z., Vol. 53, pp. 463-487 (1951).
Year 2020,
Volume: 3 Issue: 1, 66 - 76, 31.01.2020
Abstract
References
- F. Başar, Summability Theory and Its Applications, Bentham Science Publishers, Istanbul, (2012).
- J. Boos, Classical and Modern Methods in Summability, Oxford University Press. New York, (2000).
- M. Buntinas, Convergent and bounded Cesaro sections in FK-spaces, Math. Z., Vol. 121, pp. 191-200 (1971).
- M. Buntinas, On Toeplitz sections in sequence spaces, Math. Proc. Cambridge Philos. Soc., Vol. 78, pp. 451-460 (1975).
- İ. Dağadur, On some subspaces of an FK-space, Math. Commun., Vol.7, pp. 15-20 (2002).
- R. Devos, Combinations of distinguished subsets and conullity, Math. Z., Vol. 192, pp. 447-451 (1986).
- D. J. Fleming and J. C. Magee, FK-multiplier spaces, Proc. Amer. Math. Soc., Vol. 125, N. 1, pp. 175-181 (1997).
- D. J. H. Garling, The beta and gama duality of sequence spaces, Proc. Cambridge Philos. Soc., Vol. 63, pp. 963-981 (1967).
- M. Mursaleen A. K. Noman, On the spaces of lamda convergent and bounded sequences, Thai J. Math., Vol. 8, N. 2, pp. 311-329 (2010).
- W. H. Ruckle, Sequence Spaces, Pitman Advanced Publishing Program, Boston, (1981).
- A. Wilansky, Summability Through Functional Analysis, North-Holland, Amsterdam, (1984).
- K. Zeller, Allgemeine eigenschaften von limitierungsverfahren, Math. Z., Vol. 53, pp. 463-487 (1951).
There are 12 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Submission Date | January 24, 2020 |
| Acceptance Date | March 2, 2020 |
| Publication Date | January 31, 2020 |
| Published in Issue | Year 2020 Volume: 3 Issue: 1 |