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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

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.

References

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  3. ON APPROXIMATE n-ARY DERIVATIONS vol.08, pp.03, 2011, https://doi.org/10.1142/S0219887811005245
  4. Hyers–Ulam–Rassias stability of a generalized Apollonius–Jensen type additive mapping and isomorphisms betweenC *-algebras vol.281, pp.3, 2008, https://doi.org/10.1002/mana.200510611
  5. Cubic derivations on Banach algebras vol.38, pp.4, 2013, https://doi.org/10.1007/s40306-013-0031-2
  6. The N-Isometric Isomorphisms in Linear N-Normed C*-Algebras vol.22, pp.6, 2006, https://doi.org/10.1007/s10114-005-0878-9
  7. Stability of the Jensen-Type Functional Equation inC∗-Algebras: A Fixed Point Approach vol.2009, 2009, https://doi.org/10.1155/2009/360432
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  9. GENERALIZED (θ, ø)-DERIVATIONS ON BANACH ALGEBRAS vol.22, pp.1, 2014, https://doi.org/10.11568/kjm.2014.22.1.139
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