On the spaces of \(\lambda \)-convergent and bounded sequences. (English) Zbl 1218.46005

Mursaleen, M.; Noman, A. K.

Thai J. Math. 8, No. 2, 311-329 (2010).

Summary: We introduce the notion of \(\lambda \)-convergent and bounded sequences. Further, we define some related BK spaces and construct their bases. Moreover, we establish some inclusion relations concerning with those spaces and determine their \(\alpha\)-, \(\beta \)- and \(\gamma \)-duals. Finally, we characterize some related matrix classes.

MSC:

46A45	Sequence spaces (including Köthe sequence spaces)
40C05	Matrix methods for summability
40H05	Functional analytic methods in summability

Keywords:

sequence spaces; \(BK\) spaces; Schauder basis; \(\alpha\)-, \(\beta\)- and \(\gamma \)-duals; matrix mappings