Matrices and norms

Abstract

We shall define the norm h(A) of a regular summability matrix A = (amn) by Two matrices are said to be b-equivalent if every bounded sequence summable by on matrix is summable by the other. If A sums all bounded sequences that are summable by B, A is said to be b-stronger than B. The norm of a method is defined as , where the inf is taken over all the matrices equivalent to for bounded sequences. These norms have been investigated by Brudno(1). One of his main results is that, if sums all bounded sequences that are summable, then In paper we shall prove the following.