摘要：
Celik, Shalla and Olgun
defined neutro-homomorphisms in neutrosophic extended triplet groups and Zhang
et al. investigated neutro-homomorphisms in neutrosophic extended triplet
groups. In this note, we apply the results on neutro-homomorphisms in
neutrosophic extended triplet groups to investigate C*-algebra homomorphisms in
unital C*-algebras. Assume that A is a unital C*-algebra with multiplication
operation ★, unit e and unitary group U(A) and that B is a
unital C*-algebra with multiplication operation ★ and unitary group U(B).
Definition 1. Let (U(A), ★) and (U(B), ★) be unitary groups of unital C*-algebras A and
B, respectively. A mapping h: U(A) →U(B) is called a neutro-*-homomorphism
if h(u★v) = h(u)★h(v), h(u*) = h(u)* for all u,v in U(A).
We obtain the following
main result.
Theorem 1. Let A and B be unital C*-algebras. Let H: A →B be a complex-linear mapping and let h: (U(A), ★) →(U(B), ★) be a neutro-*-homomorphism.
If H|_U(A) = h, then H : A→B is a C*-algebra
homomorphism.
Further, we introduce
and solve bi-additive functional inequalities and prove the Hyers-Ulam stability
of the bi-additive functional inequalities in complex Banach spaces. This is
applied to investigate b-derivations on C*-algebras, Lie C*-algebras and JC*-algebras,
and derivations on C*-algebras, Lie C*-algebras and JC*-algebras associated
with the bi-additive functional inequalities. Moreover, we study biderivations
on C*-ternary algebras and C*-triple systems associated with the bi-additive
functional inequalities.
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