INVARIANT-MEANS AND SOME MATRIX TRANSFORMATIONS

Let l(infinity), c, c0 be the Bannock spaces of bounded, convergent an d null sequences respectively. Sigma is an injection of the set of pos itive integers into itself having no finite orbits and T, the operator defined on l(infinity) by Tx (n) = x (sigman). A positive linear func tional L with \\L\\ = 1, is called a sigma-mean if L(x) = L(Tx) for al l x in l(infinity). A sequence x is said to be sigma-convergent, denot ed x is-an-element-of V(sigma) if L(x) takes the same value, called si gma-lim x, for all sigma-means. In this paper we characterize the matr ices A is-an-element-of (l1, V(sigma)) and also study some new sequenc e spaces l(sigma) and m(sigma).