Prof.  Choonkil  Park
Hanyang University,  Republic of Korea

Title: Neutrosophic extended triplet groups and applications

Abstract:

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.

Biography:

Chun-Gil Park. He has accomplished his doctoral degree in Mathematics from the University of Maryland and is currently working as a professor at Hanyang University. He is working for several journals such as Journal of Nonlinear Science and Applications and Journal of Computational Analysis and Applications as the associate editors and Journal of Nonlinear Analysis and Applications as the Editor-in-Chief. His main research topics include operator algebras, functional inequalities, functional equations, non-commutative geometry, fixed point theory and fuzzy mappings. He has published a number of academic articles on international journals related to operator algebras, functional inequalities, functional equations, non-commutative geometry, soft and rough set, fixed point theory and fuzzy mappings. Within the last twenty years, he has successfully published more than 500 articles on SCI-E journals.