We investigate linear operators between C^⁎-algebras which approximately preserve involution and orthogonality, the latter meaning that for some $\epsilon >0$ we have $\Vert \varphi (x)\varphi (y)\Vert ⩽\epsilon \Vert x\Vert \Vert y\Vert$ for all positive $x,y$ with $xy=0$. We establish some structural properties of such maps concerning approximate Jordan-like equations and almost commutation relations. In some situations (e.g. when the codomain is finite-dimensional), we show that ϕ can be approximated by an approximate Jordan ^⁎-homomorphism, with both errors depending only on $\Vert \varphi \Vert$ and ε.

中文翻译：

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^C⁎-代数之间的近似零映射

我们研究了^C⁎代数之间的线性算子，这些算子大致保留了对合和正交性，后者意味着对于某些$\epsilon >0$ 我们有 $\Vert \varphi （X）\varphi （ÿ）\Vert ⩽\epsilon \Vert X\Vert \Vert ÿ\Vert$ 对于所有积极的 $X，ÿ$ 和 $Xÿ=0$。我们建立了这类映射的一些结构性质，涉及近似的约旦式方程和几乎换向关系。在某些情况下（例如，当陪域是有限维），我们表明，φ可以通过近似乔丹近似^⁎ -homomorphism，与仅依赖于这两个错误$\Vert \varphi \Vert$和ε。