Bounded Approximate Identities in Ternary Banach Algebras

الملخص EN

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.