ε-orthogonality preserving pairs of mappings on Hilbert C*-modules
Publish place: The Journal of Algebra and Related Topics، Vol: 10، Issue: 2
Publish Year: 1401
نوع سند: مقاله ژورنالی
زبان: English
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JR_JART-10-2_005
تاریخ نمایه سازی: 21 تیر 1403
Abstract:
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.
Authors
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