SOME CLASSES OF MATRIX TRANSFORMS CONNECTED WITH SUBSPACES OF MADDOX SPACES DEFINED BY SPEEDS OF CONVERGENCE

Abstract

Let X,Y be two sets of sequences with real or complex entries, and (X,Y) the set of matrices (with real or complex entries) to map X into Y. Let λ and µ be speeds of the convergence, i.e.; monotonically increasing positive sequences. In this paper, we give necessary and sufficient conditions for a matrix A ∈ (X,Y), if X is the subset of the set of convergent sequences defined by λ, and Y is the subset of the certain Maddox space defined by µ.