Matrix Transformations Between FK-Spaces and the Sequence Spaces m(φ) and n(φ)

In this paper, we characterize the matrix classes (X, m(φ)) and (X, n(φ)), where X is any arbitrary FK space and m(φ) and n(φ) are BK spaces introduced by Sargent (J. London Math. Soc.35 (1960), 161-170). We also deduce some important corollaries for the classes (m(φ), m(ψ)), (m(φ), n(ψ)), (n(φ), m(ψ)), (n(φ), n(ψ)), (l(p), m(φ)), and (l(p), n(φ)).