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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 | ||
آمار تعداد مشاهده مقاله: 140 تعداد دریافت فایل اصل مقاله: 250 |