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

In this paper, we introduce the double sequence spaces (...(p))2P, (0...(p))2P, (...(p))2PB, (0...(p))2PB, ...(p) and (...(p))2P. The inclusion relations among these spaces are obtained. We also characterize the matrix classes (ℓ2∞(p), 0c2PB), (ℓ2∞(p), c2PB), (ℓ2∞(p), c2P); ((...(p))2PB, c2PB) and ((...(p))2PB, c2PB)reg. Furthermore, we define the statistical core of a real-valued double sequence belonging to the more general class ℓ2∞(p) and study the statistical core inequalities related to this new type of statistical core by using our matrix classes ((...(p))2PB, c2PB) and ((...(p))2PB, c2PB)reg. [ABSTRACT FROM AUTHOR]