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Functions Preserving the Biadditivity
Results in Mathematics ( IF 2.2 ) Pub Date : 2020-05-23 , DOI: 10.1007/s00025-020-01206-3
Radosław Łukasik , Paweł Wójcik

In this paper we consider the generalization of the orthogonality equation. Let S be a semigroup, and let H , X be abelian groups. For two given biadditive functions $$A:S^2\rightarrow X$$ A : S 2 → X , $$B:H^2\rightarrow X$$ B : H 2 → X and for two unknown mappings $$f,g:S\rightarrow H$$ f , g : S → H the functional equation $$\begin{aligned} B(f(x),g(y))=A(x,y) \end{aligned}$$ B ( f ( x ) , g ( y ) ) = A ( x , y ) will be solved under quite natural assumptions. This extends the well-known characterization of the linear isometry.

中文翻译:

保持双可加性的函数

在本文中,我们考虑了正交方程的推广。令 S 为半群,令 H , X 为阿贝尔群。对于两个给定的双加函数 $$A:S^2\rightarrow X$$ A : S 2 → X , $$B:H^2\rightarrow X$$ B : H 2 → X 以及两个未知映射 $$f ,g:S\rightarrow H$$ f , g : S → H 函数方程 $$\begin{aligned} B(f(x),g(y))=A(x,y) \end{aligned} $$ B ( f ( x ) , g ( y ) ) = A ( x , y ) 将在非常自然的假设下求解。这扩展了线性等距的众所周知的特征。
更新日期:2020-05-23
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