Bounded Approximate Identities in Ternary Banach Algebras

Abstract

Let A be a ternary Banach algebra. We prove that if A has a left-bounded approximating set, then A has a left-bounded approximate identity. Moreover, we show that if A has bounded left and right approximate identities, then A has a bounded approximate identity. Hence, we prove Altman’s Theorem and Dixon’s Theorem for ternary Banach algebras.