MATRIX TRANSFORMS OF SUBSPACES OF SUMMABILITY DOMAINS OF NORMAL MATRICES DETERMINED BY SPEED

Abstract

Let X, Y be two subspaces of summability domains of matrices with real or complex entries defined 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 map X into Y , where X is the subspaces of summability domain of a normal matrix A defined by the speed λ and Y is the subspace of a lower triangular matrix B defined by the speed µ. As an application we consider the case if A is the Riesz method (R, p_n).