MATRIX TRANSFORMS OF SUBSPACES OF SUMMABILITY DOMAINS OF MATRICES DEFINED BY SPEED OF CONVERGENCE

Abstract

Let X,Y be two subspaces of summability domains of matrices with real or complex entries determined by speeds of the convergence, i.e.; by monotonically increasing positive sequences λ and µ. In this paper, we give necessary and sufficient conditions for a matrix M (with real or complex entries) to transform X into Y, where X is the subspace of summability domain of a λ-reversible or a normal or a λ-perfect matrix A defined by the speed λ and Y is the subspace of a lower triangular matrix B defined by the speed µ.