Empty-cored sequences in Banach spaces

Abstract

The purpose of the present paper is to describe sequences in Banach spaces in terms of Knopp core. For matrix summability methods, the conditions forcore-shrinkingness are also given. In investigations of core inclusions and several other summability problems in Banach spaces it is vital to be aware ofelements with empty cores. Empty-cored sequences that remain empty-cored under transformation by an arbitrary regular matrix method are described.