Bulletin of Australian Mathematical Society, ( ISI ), Volume (99), No (3), Year (2019-6) , Pages (485-496)

Title : ( APPROXIMATELY ANGLE PRESERVING MAPPINGS )

Authors: Mohammad Sal Moslehian , Ali Zamani , Pawel Wojcik ,

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Abstract

‎In this paper‎, ‎we present some characterizations of linear mappings‎, ‎which preserve vectors at a specific angle‎. ‎We introduce the concept of $-varepsilon‎, ‎c-$-angle preserving mappings for $|c|<1$ and $0leq varepsilon < 1‎ + ‎|c|$‎. ‎In addition‎, ‎we define $widehat{varepsilon},-T‎, ‎c-$ as the ``smallest\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\'\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\' number $varepsilon$ for which $T$ is $-varepsilon‎, ‎c-$-angle preserving mapping‎. ‎We state some properties of the function $widehat{varepsilon},-.‎, ‎c-$‎, ‎and then propose an exact formula for $widehat{varepsilon},-T‎, ‎c-$ in terms of the norm $|T|$ and the minimum modulus $[T]$ of $T$‎. ‎Finally‎, ‎we characterize the approximately angle preserving mappings‎.

Keywords

, ‎orthogonality; norm, parallelism; Schatten p, norm; disjoint supports; trace; compact operator.
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@article{paperid:1071069,
author = {Sal Moslehian, Mohammad and Ali Zamani and Pawel Wojcik},
title = {APPROXIMATELY ANGLE PRESERVING MAPPINGS},
journal = {Bulletin of Australian Mathematical Society},
year = {2019},
volume = {99},
number = {3},
month = {June},
issn = {0004-9727},
pages = {485--496},
numpages = {11},
keywords = {‎orthogonality; norm-parallelism; Schatten p-norm; disjoint supports; trace; compact operator.},
}

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%0 Journal Article
%T APPROXIMATELY ANGLE PRESERVING MAPPINGS
%A Sal Moslehian, Mohammad
%A Ali Zamani
%A Pawel Wojcik
%J Bulletin of Australian Mathematical Society
%@ 0004-9727
%D 2019

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