Empty-cored sequences in Banach spaces
Keywords:Knopp core, core, core-shrinking matrix method
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.