Jordan Maps on Associative Algebras

Abstract

Let 𝒜 and 𝒜′ are associative algebras over the field ℚ of rational numbers and k ∈ ℚ. In this paper, we investigate the additivity of maps φ from 𝒜 onto 𝒜′ that are bijective and satisfy for all a, b ∈ 𝒜. If 𝒜 is a unital prime algebra containing a non-trivial idempotent, or 𝒜 is a unital algebra which has a system of matrix units, or 𝒜 is a standard operator algebra on a Banach space, then we can conclude that φ is additive.