Title : ( An extension of orthogonality relations based on norm derivatives )
Authors: Ali Zamani , Mohammad Sal Moslehian ,
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Abstract
We introduce the relation ρλ-orthogonality in the setting of normed spaces as an extension of some orthogonality relations based on norm derivatives and present some of its essential properties. Among other things, we give a characterization of inner product spaces via the functional ρλ. Moreover, we consider a class of linear mappings preserving this new kind of orthogonality. In particular, we show that a linear mapping preserving ρλ-orthogonality has to be a similarity, that is, a scalar multiple of an isometry.
Keywords
, orthogonality relation, normed space, norm derivative, orthogonality
@article{paperid:1074878,
author = {Ali Zamani and Sal Moslehian, Mohammad},
title = {An extension of orthogonality relations based on norm derivatives},
journal = {Quarterly Journal of Mathematics},
year = {2019},
volume = {70},
number = {2},
month = {June},
issn = {0033-5606},
pages = {379--393},
numpages = {14},
keywords = {orthogonality relation; normed space; norm derivative; orthogonality},
}
%0 Journal Article
%T An extension of orthogonality relations based on norm derivatives
%A Ali Zamani
%A Sal Moslehian, Mohammad
%J Quarterly Journal of Mathematics
%@ 0033-5606
%D 2019
