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Sahleh, A., Olyani Nezhad, F.. (1401). ε-orthogonality preserving pairs of mappings on Hilbert C*-modules. فیزیولوژی و بیوتکنولوژی آبزیان, 10(2), 51-60. doi: 10.22124/jart.2022.21879.1386
A. Sahleh; F. Olyani Nezhad. "ε-orthogonality preserving pairs of mappings on Hilbert C*-modules". فیزیولوژی و بیوتکنولوژی آبزیان, 10, 2, 1401, 51-60. doi: 10.22124/jart.2022.21879.1386
Sahleh, A., Olyani Nezhad, F.. (1401). 'ε-orthogonality preserving pairs of mappings on Hilbert C*-modules', فیزیولوژی و بیوتکنولوژی آبزیان, 10(2), pp. 51-60. doi: 10.22124/jart.2022.21879.1386
Sahleh, A., Olyani Nezhad, F.. ε-orthogonality preserving pairs of mappings on Hilbert C*-modules. فیزیولوژی و بیوتکنولوژی آبزیان, 1401; 10(2): 51-60. doi: 10.22124/jart.2022.21879.1386

ε-orthogonality preserving pairs of mappings on Hilbert C*-modules

Journal of Algebra and Related Topics
دوره 10، شماره 2، اسفند 2022، صفحه 51-60    اصل مقاله (317.61 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22124/jart.2022.21879.1386
نویسندگان
A. Sahleh* 1؛ F. Olyani Nezhad2
1Department of Mathematic, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.
2Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
چکیده
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} $,
\begin{align*}
    \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.
\end{align*}
Our results generalize the known ones in the context of Hilbert spaces.
کلیدواژه‌ها
ε-orthogonality preserving mappings؛ local mappings؛ Hilbert C*-modules
مراجع
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