Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Approximate *-derivations and approximate quadratic *-derivations on C*-algebra | Jang and Park Journal of Inequalities and Applications 2011 2011 55 http content 2011 1 55 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Approximate -derivations and approximate quadratic -derivations on C -algebras Sun Young Jang 1 and Choonkil Park2 Correspondence baak@hanyang. department of Mathematics Research Institute for Natural Sciences Hanyang University Seoul 133-791 Korea Full list of author information is available at the end of the article Springer Abstract In this paper we prove the stability of -derivations and of quadratic -derivations on Banach -algebras. We moreover prove the superstability of -derivations and of quadratic -derivations on C -algebras. 2000 Mathematics Subject Classification 39B52 47B47 46L05 39B72. Keywords -derivation quadratic -derivation C -algebra stability superstability 1 Introduction and preliminaries Suppose that A is a complex Banach -algebra- A C-linear mapping 8 D 8 A is said to be a derivation on A if b ab d a b aỏ b for all a b e A where D ỏ is a domain of Ỏ and D d is dense in A- If d satisfies the additional condition ỏ a ỏ a for all a e A then Ỏ is called a -derivation on A- It is well known that if A is a C -algebra and D d is A then the derivation Ỏ is bounded- A C -dynamical system is a triple A G a consisting of a C -algebra A a locally compact group G and a pointwise norm continuous homomorphism a of G into the group Aut A of -automorphisms of A- Every bounded -derivation Ỏ arises as an infinitesimal generator of a dynamical system for R. In fact if Ỗ is a bounded -derivation of A on a Hilbert space H then there exists an element h in the enveloping von Neumann algebra A such that 8 x adih x for all x e A- If for each t e R at is defined by at x eith xe-ith for all x e A then at is a -automorphism of A induced by unitaries Ut eith for each t e R- The action a R Aut A t at is a strongly continuous one-parameter group of .
