Zeitschrift fur Analysis und ihre Anwendung, ( ISI ), Volume (34), No (4), Year (2015-12) , Pages (485-500)

Title : ( Angle Preserving Mappings )

Authors: Ali Zamani , Mohammad Sal Moslehian , Michael Frank ,

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In this paper, we give some characterizations of orthogonality preserving mappings between inner product spaces. Furthermore, we study the linear mappings that preserve some angles. One of our main results states that if $\mathcal{X}, \mathcal{Y}$ are real inner product spaces and $\theta\in(0, \pi)$, then an injective nonzero linear mapping $T:\mathcal{X}\longrightarrow \mathcal{Y}$ is a similarity whenever (i) $x\underset{\theta}{\angle} y\, \Leftrightarrow \,Tx\underset{\theta}{\angle} Ty$ for all $x, y\in \mathcal{X}$; (ii) for all $x, y\in \mathcal{X}$, $\|x\|=\|y\|$ and $x\underset{\theta}{\angle} y$ ensure that $\|Tx\|=\|Ty\|$. We also investigate orthogonality preserving mappings in the setting of inner product $C^{*}$-modules. Another result shows that if $\mathbb{K}(\mathscr{H})\subseteq\mathscr{A}\subseteq\mathbb{B}(\mathscr{H})$ is a $C^{*}$-algebra and $T\,:\mathscr{E}\longrightarrow \mathscr{F}$ is an $\mathscr{A}$-linear mapping between inner product $\mathscr{A}$-modules, then $T$ is orthogonality preserving if and only if $|x|\leq|y|\, \Rightarrow \,|Tx|\leq|Ty|$ for all $x, y\in \mathscr{E}$.


, Orthogonality preserving mapping, angle, inner product space, inner product $C^*$-module
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author = {Zamani, Ali and Sal Moslehian, Mohammad and Michael Frank},
title = {Angle Preserving Mappings},
journal = {Zeitschrift fur Analysis und ihre Anwendung},
year = {2015},
volume = {34},
number = {4},
month = {December},
issn = {0232-2064},
pages = {485--500},
numpages = {15},
keywords = {Orthogonality preserving mapping; angle; inner product space; inner product $C^*$-module},


%0 Journal Article
%T Angle Preserving Mappings
%A Zamani, Ali
%A Sal Moslehian, Mohammad
%A Michael Frank
%J Zeitschrift fur Analysis und ihre Anwendung
%@ 0232-2064
%D 2015