SOME NEW SPACES OF DOUBLE SEQUENCES AND THE STATISTICAL CORE ON l2?(p)

Abstract

In this paper, we introduce the double sequence spaces ((c) over bar (p))(2)(P), ((0)(c) over bar (p))(2)(P), ((c) over bar (p))(2)(PB), ((0)(c) over bar (p))(2)(PB), (l) over bar (infinity)(2)(p) and ((c) over bar*(p))(2)(P). The inclusion relations among these spaces are obtained. We also characterize the matrix classes ((l) over bar (infinity)(2)(p),(0)c(2)(PB)), (l(2)(infinity)(p), c(2)(PB)), (l(2)(infinity)(p), c(2)(P)), ((c) over bar (p))(2)(PB), c(2)(PB)) and ((c) over bar (p))(2)(PB), c(2)(PB))(reg). Furthermore, we define the statistical core of a real-valued double sequence belonging to the more general class l(2)(infinity)(p) and study the statistical core inequalities related to this new type of statistical core by using our matrix classes ((c) over bar (p))(2)(PB), c(2)(PB)) and ((c) over bar (p))(2)(PB), c(2)(PB) )(reg).