Le théorème de Hua pour les algèbres artiniennes simples

A Note on 2-Local Maps

“…This result is connected with the well-known Hua theorem [14] and it generalizes some results of [5,10].…”

“…If we can claim λ ∈ Z, then we will have ϕ(a −1 )ϕ(a) = z −1 α(a −1 )α(a) = z −1 z = 1 for all invertible a ∈ M n (K). Hence, ϕ is an automorphism or an anti-automorphism in light of [10] and so the proof will be complete.…”

“…or an anti-automorphism in light of [10] and so the proof will be complete. Let x, y ∈ M n (K) be invertible elements such that x − y −1 is invertible.…”

“…This result was reformulated by Artin as: any bijective additive map α on a division ring K satisfying α(a −1 ) = α(a) −1 and α(1) = 1 is an automorphism or an antiautomorphism [1, Theorem 1.15]. The same result was established for the n × n matrix rings over a division ring K in case when K = GF(2), the Galois field of two elements [10]. In [5], the authors removed the condition of α(1) = 1 in Hua's result and prove the following.…”

Approximate Preservers on Banach Algebras andC*-Algebras

“…A well known formulation of the celebrated Hua's theorem [1] asserts that every bijective additive map : → on a division ring such that (1) = 1 and ( −1 ) = ( ) −1 for every invertible element is either an automorphism or an antiautomorphism. This result was later moved to matrix algebras in [2] and finally extended to Banach algebras in [3] (see also [4]). In [3], the author called the previous relation strongly preserving invertibility.…”