ON HOMOMORPHISMS BETWEEN C*-ALGEBRAS AND LINEAR DERIVATIONS ON C*-ALGEBRAS


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Abstract

It is shown that every almost linear Pexider mappings f, g, h from a unital C*-algebra 𝒜 into a unital C*-algebra ℬ are homomorphisms when f(2nuy) = f(2nu) f(y), g(2nuy) = g(2nu) g(y) and h(2nuy) = h(2nu) h(y) hold for all unitaries u ∈ 𝒜, all y ∈ 𝒜, and all n ∈ ℤ, and that every almost linear continuous Pexider mappings f, g, h from a unital C*-algebra 𝒜 of real rank zero into a unital C*-algebra ℬ are homomorphisms when f(2nuy) = f(2nu) f(y), g(2nuy) = g(2nu) g(y) and h(2nuy) = h(2nu) h(y) hold for all u ∈ {v ∈ 𝒜: v = v* and v is invertible}, all y ∈ 𝒜 and all n ∈ ℤFurthermore, we prove the Cauchy-Rassias stability of *-homomorphisms between unital C*-algebras, and ℂ-linear *-derivations on unital C*-algebras.

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