MATRIX TRANSFORMS BETWEEN SEQUENCE SPACES DEFINED BY SPEEDS OF CONVERGENCE

Abstract

Let X,Y be two sequence spaces defined by speeds of the convergence, i.e.; by monotonically increasing
positive sequences. In this paper necessary and sufficient conditions for a matrix A (with real or complex
entries) to be transform from X into Y have been found. Also the analogue of the well known result of
Steinhaus, which states that a regular matrix cannot transform each bounded sequence into convergent
sequence, for the sequence spaces defined by the speeds of convergence has been proved.