ON SOME NEW FK SPACES OBTAINED FROM SUMMABILITY MATRIX

Öz

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.

Anahtar Kelimeler

• FK-spaces,matrix methods,beta-gama-f-duality

Kaynakça

1. F. Başar, Summability Theory and Its Applications, Bentham Science Publishers, Istanbul, (2012).
2. J. Boos, Classical and Modern Methods in Summability, Oxford University Press. New York, (2000).
3. M. Buntinas, Convergent and bounded Cesaro sections in FK-spaces, Math. Z., Vol. 121, pp. 191-200 (1971).
4. M. Buntinas, On Toeplitz sections in sequence spaces, Math. Proc. Cambridge Philos. Soc., Vol. 78, pp. 451-460 (1975).
5. İ. Dağadur, On some subspaces of an FK-space, Math. Commun., Vol.7, pp. 15-20 (2002).
6. R. Devos, Combinations of distinguished subsets and conullity, Math. Z., Vol. 192, pp. 447-451 (1986).
7. D. J. Fleming and J. C. Magee, FK-multiplier spaces, Proc. Amer. Math. Soc., Vol. 125, N. 1, pp. 175-181 (1997).
8. D. J. H. Garling, The beta and gama duality of sequence spaces, Proc. Cambridge Philos. Soc., Vol. 63, pp. 963-981 (1967).

9. 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).
10. W. H. Ruckle, Sequence Spaces, Pitman Advanced Publishing Program, Boston, (1981).
11. A. Wilansky, Summability Through Functional Analysis, North-Holland, Amsterdam, (1984).
12. K. Zeller, Allgemeine eigenschaften von limitierungsverfahren, Math. Z., Vol. 53, pp. 463-487 (1951).