Abstract
Let [Formula: see text] and [Formula: see text] be two unital [Formula: see text]-algebras with unit [Formula: see text]. It is shown that the mapping [Formula: see text] which preserves arithmetic mean and Jordan triple product is a difference of two Jordan homomorphisms provided that [Formula: see text]. The structure of [Formula: see text] is more refined when [Formula: see text] or [Formula: see text]. Furthermore, if [Formula: see text] is a [Formula: see text]-algebra of real rank zero and [Formula: see text] is additive and preserves absolute value of product, then [Formula: see text] such that [Formula: see text] (respectively, [Formula: see text]) is a complex linear (respectively, antilinear) ∗-homomorphism.
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