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


Candan M.

ADVANCES IN DIFFERENCE EQUATIONS, 2014 (SCI İndekslerine Giren Dergi) identifier identifier

Özet

What stands out in this article is the sequence spaces of a new brand c(0)(lambda)((B) over tilde) and c(lambda)((B) over tilde), derived by using a double sequential band matrix B(T-,'s-) which generalizes the previous work of Sonmez and Baar (Abstr. Appl. Anal. 2012:435076,2012), where (r(n))(n=0)(infinity) and (s(n))(n=0)(infinity) 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 co and c, respectively. Then, some inclusion relations are derived to determine the alpha-, beta- and gamma-duals of these spaces. Next, their Schauder bases are constructed. In conclusion, some matrix classes from the spaces c(0)(lambda)((B) over tilde) and c(lambda)((B) over tilde) to the spaces l(p), C-o 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.