Abstract.
It is shown that every almost linear mapping \( h:{\user1{\mathcal{A}}} \to {\user1{\mathcal{B}}} \) of a unital Poisson JC*-algebra \( {\user1{\mathcal{A}}} \) to a unital Poisson JC*-algebra \( {\user1{\mathcal{B}}} \) is a Poisson JC*-algebra homomorphism when h(2n uоy) = h(2n u) о h(y), h(3n uо y) = h(3n u) о h(y) or h(q n u о y) = h(q n u) о h(y) for all \( y \in {\user1{\mathcal{A}}} \), all unitary elements \( u \in {\user1{\mathcal{A}}} \) and n = 0, 1, 2, · · · , and that every almost linear almost multiplicative mapping \( h:{\user1{\mathcal{A}}} \to {\user1{\mathcal{B}}} \) is a Poisson JC*-algebra homomorphism when h(2x) = 2h(x), h(3x) = 3h(x) or h(qx) = qh(x) for all \( x \in {\user1{\mathcal{A}}} \). Here the numbers 2, 3, q depend on the functional equations given in the almost linear mappings or in the almost linear almost multiplicative mappings.
Moreover, we prove the Cauchy–Rassias stability of Poisson JC*-algebra homomorphisms in Poisson JC*-algebras.
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*This work was supported by grant No. R05-2003-000-10006-0 from the Basic Research Program of the Korea Science & Engineering Foundation.
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Park*, CG. Homomorphisms between Poisson JC*-Algebras. Bull Braz Math Soc, New Series 36, 79–97 (2005). https://doi.org/10.1007/s00574-005-0029-z
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DOI: https://doi.org/10.1007/s00574-005-0029-z