Domain of the double sequential band matrix in the spaces of convergent and null sequences

Murat Candan

doi:10.1186/1687-1847-2014-163

Abstract

What stands out in this article is the sequence spaces of a new brand c 0 λ ( B ˜ ) and c λ ( B ˜ ), derived by using a double sequential band matrix B( r ˜ , s ˜ ) which generalizes the previous work of Sönmez and Başar (Abstr. Appl. Anal. 2012:435076, 2012), where ( r n ) n = 0 ∞ and ( s n ) n = 0 ∞ are given convergent sequences of positive real numbers. The aforementioned spaces are in fact the BK-spaces of non-absolute type. Moreover, they are norm isomorphic to the spaces c 0 and c, respectively. Then, some inclusion relations are derived to determine the α-, β- and γ-duals of these spaces. Next, their Schauder bases are constructed. In conclusion, some matrix classes from the spaces c 0 λ ( B ˜ ) and c λ ( B ˜ ) to the spaces ℓ p , c 0 and c are characterized. When compared with the corresponding results in the literature, it is seen that the results of the present study are more general and more inclusive.MSC:46A45, 40C05.

Highlights

What stands out in this article is the sequence spaces of a new brand c0λ(B) and cλ(B), derived by using a double sequential band matrix B( ̃r, s) which generalizes the previous work of Sönmez and Basar
A sequence is bounded if the set of its terms is bounded
Any vector subspace of ω = ω(K) = KN is known as a sequence space

Summary

Introduction

What stands out in this article is the sequence spaces of a new brand c0λ(B) and cλ(B), derived by using a double sequential band matrix B( ̃r, s) which generalizes the previous work of Sönmez and Basar We proceed slightly differently to Kızmaz [ ] and the other authors following him, and employ a technique of obtaining a new sequence space by means of the matrix domain of a triangle limitation method. It is time to give another very useful result for new difference sequence spaces defined above.

Results

Conclusion