Some Topological and Geometric Properties of the Domain of the Double Sequential Band Matrix B(r;s) in the Sequence Space (p)

The sequence space (p) was introduced by Maddox [Spaces of strongly summable sequences, Quart. J. Math.Oxford (2)18(1967), 345–355]. In the present paper, the sequence space(eB; p) of non-absolute type, the domain of the double sequential band matrix B(er;es) in the sequence space (p), is introduced. Furthermore, the a-, b- and g-duals of the space(eB; p) are determined, and the Schauder basis is given. The classes of matrix transformations from the space (eB; p) to the spaces¥, f and c are characterized. Additionally, the characterizations of some other matrix transformations from the space (eB; p) to the Euler, Riesz, difference, etc., sequence spaces are obtained by means of a given lemma. Finally, some properties of the space(eB; p) are examined.