Take Jordan Derivations On C, ~ * - Semi-inner Product Stability And Joran Algebra And B (h) ~ S-dual Joran Derivation,

Recently,the stability problem of functional equations gets more attention. In 1940,Ulam posed the first stability problem cencerning the stability of group homomorphism. It is on what conditions that an approximately additive mapping can be approached by an additive mapping.From then on,there are a lot of generalized results concerning this problem. And all of these results are known today as Hyers-Ulam-Rassias stability of functional equations.Therefore the generalized stability of C*-semi-inner on C*-module is valuable to be considered.The first part of this paper aims to give conditions that can make an linear mapping on left C*-modules be approximated by a C*-semi-inner.Jordan algebra is one of the important operator algebras and Jordan deriva-tion is an important mapping.In the second part of this paper, a theorem is given as follows. Let A be a unitial Jordan algebra and A has an nontrival idempotent p(p≠1,p≠0) which satisfies that the Peirce decomposition of A with respect to p, A=A1⊕A1/2⊕A0,ai∈Ai(i=0,1)satisfies that arbitrary t1/2 E A1/2, then ai=0. If d is any multiplicative Jordan derivation of A which satisfies that d(p)=0,then d is additive.The last part of this paper gives the sufficient and necessary conditions which make bilinear mappings on selfadjiont operator Jordan algebra B(H)S be Jordan biderivations or Jordan generalized biderivations.