$sigma$-regular matrices and A $sigma$- core theorem for double sequences

Abstract

The famous Knopp Core of a single sequence was extended to the P- core of a double sequence by R.F. Patterson. Recently, the MR-core and σ-core of real bounded double sequences have been introduced and some inequalities analogues to those for Knoop’s Core Theorem have been studied. The aim of this paper is to characterize a class of four-dimensional matrices, and so to obtain necessary and sufficient conditions for a new inequality related to the P- and σ-cores.