In this paper, we present results concerning orthogonality in Hilbert $C^{\ast }$-modules. Moreover, for a $C^{\ast }$-algebra $\mathcal{A}$, we prove theorems concerning the multi-$\mathcal{A}$-linearity and its preservation by$\mathcal{A}$-linear operators. New version of solution of the orthogonality equation on Hilbert $C^{\ast }$-modules and mappings preserving orthogonality are also investigated.

中文翻译：

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正交性 Hilbert 𝒜-模和算子保持多重𝒜-线性

在本文中，我们提出了有关 Hilbert 正交性的结果$C^{＊}$-模块。此外，对于一个$C^{＊}$-代数$\mathcal{A}$，我们证明了关于多的定理$\mathcal{A}$- 线性及其保存$\mathcal{A}$- 线性运算符。希尔伯特正交方程的新解$C^{＊}$- 还研究了保持正交性的模块和映射。