Matrix mappings on multiplier sequence spaces (Q2861320)

Let \(\lambda ,\mu \) be non-zero sequences of scalars and \(E,F\) be scalar sequence spaces. If \(A=[a_{ij}]\) is an infinite matrix which maps \(E\) into \(F \), write \(A\in (E,F)\). Set \(E(\lambda )=\{z:\lambda z\in E\}\), where \(\lambda z\) is the coordinate product of the sequences \(z\) and \(\lambda \). The author shows that \(A\in (E(\lambda ),F(\mu ))\) iff \(A(\mu ,\lambda^{-1})=[\frac{1}{\lambda _{j}}a_{ij}\mu _{i}]\in (E,F)\), and then uses this result to give characterizations of matrix mappings between classical multiplier sequence spaces as well as other related results.