Homomorphisms between Poisson JC*-Algebras |
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Authors: | Chun-Gil Park |
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Affiliation: | (1) Department of Mathematics, Chungnam National University, Daejeon 305–764, SOUTH KOREA |
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Abstract: | It is shown that every almost linear mapping of a unital Poisson JC*-algebra to a unital Poisson JC*-algebra is a Poisson JC*-algebra homomorphism when h(2 n uy) = h(2 n u) h(y), h(3 n u y) = h(3 n u) h(y) or h(q n u y) = h(q n u) h(y) for all , all unitary elements and n = 0, 1, 2, · · · , and that every almost linear almost multiplicative mapping is a Poisson JC*-algebra homomorphism when h(2x) = 2h(x), h(3x) = 3h(x) or h(qx) = qh(x) for all . 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.*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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Keywords: | Poisson JC*-algebra homomorphism Poisson JC*-algebra stability linear functional equation |
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