Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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HOMOMORPHISMS BETWEEN C*-ALGEBRAS ASSOCIATED WITH THE TRIF FUNCTIONAL EQUATION AND LINEAR DERIVATIONS ON C*-ALGEBRAS

  • Park, Chun-Gil (Department of Mathematics Chungnam National University) ;
  • Hou, Jin-Chuan (Department of Mathematics Shanxi Teachers University, Department of Mathematics Shanxi University)
  • Published : 2004.05.01
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Abstract

It is shown that every almost linear mapping h : A\longrightarrowB of a unital $C^{*}$ -algebra A to a unital $C^{*}$ -algebra B is a homomorphism under some condition on multiplication, and that every almost linear continuous mapping h : A\longrightarrowB of a unital $C^{*}$ -algebra A of real rank zero to a unital $C^{*}$ -algebra B is a homomorphism under some condition on multiplication. Furthermore, we are going to prove the generalized Hyers-Ulam-Rassias stability of *-homomorphisms between unital $C^{*}$ -algebras, and of C-linear *-derivations on unital $C^{*}$ -algebras./ -algebras.

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References

  1. J. Funct. Anal. v.99 $C^*$- algebras of real rank zero L.Brown;G.Pedersen https://doi.org/10.1016/0022-1236(91)90056-B
  2. J. Math. Anal. Appl. v.184 A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings P.Gavruta https://doi.org/10.1006/jmaa.1994.1211
  3. J. London Math. Soc. v.37 no.2 Approximately multiplicative maps between Banach algebras B.E.Johnson https://doi.org/10.1112/jlms/s2-37.2.294
  4. Math. Scand. v.57 Means and convex combinations of unitary operators R.V.Kadison;G.Pedersen
  5. Elementary Theory Fundamentals of the Theory of Operator Algebras R.V.Kadison;J.R.Ringrose
  6. J. Math. Anal. Appl. v.278 Modified Trif's functional equations in Banach modules over a$C^*$-algebra and approximate algebra homomorphisms C.Park https://doi.org/10.1016/S0022-247X(02)00573-5
  7. Proc. Amer. Math. Soc. v.72 On the stability of the linear mapping in Banach spaces Th.M.Rassias https://doi.org/10.2307/2042795
  8. J. Math. Anal. Appl. v.272 On the stability of a functional equation deriving from an inequality of Popoviciu for convex functions T.Trif https://doi.org/10.1016/S0022-247X(02)00181-6

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