Quarterly Journal of Mathematics, Volume (70), No (2), Year (2019-6) , Pages (379-393)
Title : ( An extension of orthogonality relations based on norm derivatives )
Authors: Ali Zamani , Mohammad Sal Moslehian ,Access to full-text not allowed by authors
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.