On conservative and coercive SM-methods

Abstract

We study the spaceCe of double sequences(xkl), satisfying lim l lim k |xkl a|=0 for some number a. In this note, using gliding hump arguments, we give necessary and sufficient conditions for a 3-dimensional matrix (i.e. SM-method) to transform every convergent or bounded sequence (xk) into the space Ce or Cbe, the space of elements in Ce with bounded columns.