University of Guilan Journal of Algebra and Related Topics 2345-3931 10 2 2022 12 01 ε-orthogonality preserving pairs of mappings on Hilbert C*-modules 51 60 5988 10.22124/jart.2022.21879.1386 EN A. Sahleh Department of Mathematic, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran. F. Olyani Nezhad Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran Journal Article 2022 03 02 Let $ \mathcal{A} $ be a standard $ C^{*} $-algebra. In this paper, we will study the continuity of $ \varepsilon $-orthogonality preserving mappings between Hilbert $ \mathcal{A} $-modules. Moreover, we will show that a local mapping between Hilbert $ \mathcal A $-modules is  $ \mathcal A $-linear. Furthermore, we will prove that for a pair of nonzero $ \mathcal A $-linear mappings $ T,S:E\longrightarrow F $, between Hilbert  $ \mathcal A $-modules, satisfying  $ \varepsilon $-orthogonality preserving property, there exists $ \gamma \in \mathbb{C} $,<br />\begin{align*}<br />    \Vert \langle T(x), S(y) \rangle-\gamma \langle x, y \rangle\Vert \leq \varepsilon \Vert T\Vert \Vert S\Vert \Vert x\Vert \Vert y \Vert,  \quad x, y \in E.<br />\end{align*}<br />Our results generalize the known ones in the context of Hilbert spaces. https://jart.guilan.ac.ir/article_5988_00fd46ef59d5c647eab0794a7bb97f3c.pdf