Generalized domination of ergodic elements in ordered Banach algebras

Let A be an ordered Banach algebra and a, b is an element of A such that 0 <= a <= b. The domination problem involves finding natural conditions under which properties of b will be inherited by a. In [12] this problem was investigated for ergodic elements, where a is an element of A is ergodic if the sequence converges in A. In this paper we consider the more general problem where the assumption 0 <= a <= b is replaced by the weaker condition +/- a <= b.