On the statistical and $\sigma $-cores
Volume 154 / 2003
Studia Mathematica 154 (2003), 29-35
MSC: Primary 40C05; Secondary 26A03, 11B05.
DOI: 10.4064/sm154-1-3
Abstract
In [11] and [7], the concepts of $\sigma $-core and statistical core of a bounded number sequence $x$ have been introduced and also some inequalities which are analogues of Knopp's core theorem have been proved. In this paper, we characterize the matrices of the class $(S \cap m, V_{\sigma })_{{\rm reg}}$ and determine necessary and sufficient conditions for a matrix $A$ to satisfy $\sigma $-core$(Ax) \subseteq {}$st-core$(x)$ for all $x \in m$.
