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 ,

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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