Triangles Which Are Bounded Operators on Ak

Abstract

A lower triangular infinite matrix is called a triangle if there are no zeros on the principal diagonal. The main result of this paper gives a minimal set of sufficient conditions for a triangle T : A(k) -> A(k) for the sequence space A(k) defined as follows: A(k) := {{s(n)} : (n=1)Sigma(infinity)n(k-1)vertical bar a(n)vertical bar(k) < infinity, a(n) = s(n) - s(n-1)}.