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A note on the linearity of an additive mapping

GAO Zhen-xia,CAO Huai-xin (College of Mathematics and Information Science,Shaanxi Normal University,Xi'an 710062,Shaanxi,China)  
Aim To introduce some concepts about the decompositions of complex number,give some results on the decompositions of complex number and study the linearity of additive mappings.Methods Operator theoretic method is used.Results It is proved that if an additive mapping f:X→Y satisfies f(μx)=μf(x)(|μ|=a0,x∈X),then f is linear.Conclusion The results is very useful for constructing a linear mapping and judging a mapping whether it is linear.
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