On multipliers in sequence spaces and a theorem of bosanquet

For sequence spaces E and F, a sequence u is an (E→F) multiplier when (xk) ε E always implies (ukxk) ε F. When E and F are matrix fields, u is often called a summability-factor sequence, and there are many classical results in such cases. We give some general results on multipliers, depending on basis arguments, and illustrate these with a discussion of a well-known theorem of Bosanquet on Cesàro summability factors with order conditions.