COMPACT MATRIX OPERATORS BETWEEN THE SPACES m(ϕ), n(ϕ) AND ℓp

We give the characterizations of the classes of matrix trans-formations (<TEX>m(φ),ₚ</TEX>), (<TEX>n(φ),ₚ</TEX>) ([5, Theorem 2]), (<TEX>ₚ,m(φ)</TEX>) ([5, Theorem 1]) and (<TEX>ₚ,n(φ)</TEX>) for <TEX>1≤p≤∞</TEX>, establish estimates for the norms of the bounded linear operators defined by those matrix transformations and characterize the corresponding subclasses of compact matrix operators.