Dual pairs of sequence spaces
Let \(E\) be a sequence space and \(S\) be a \(K\)-space on which a sum is defined in the sense of Ruckle and let \(E^S\) be the linear space of all corresponding factor spaces. The authors define and investigate dual pairs \((E, E^S)\). In this connection, they study the SK-property which corresponds to the weak sectional convergence (SAK-property) and the so-called quasi-matrix \(A.\) They study the continuity of \( A\) and a natural topological structure of the domain \(F_A\) of \(A\), where \(F\) is a \(K\)-space. They prove some general inclusion theorems which enable them to deduce several known inclusion results in the field.
scientific article; zbMATH DE number 1750378