This is an announcement for the paper “Characterizations of smooth spaces by $\rho_*$-orthogonality” by Mohammad Sal Moslehianhttps://arxiv.org/find/math/1/au:+Moslehian_M/0/1/0/all/0/1, Ali Zamanihttps://arxiv.org/find/math/1/au:+Zamani_A/0/1/0/all/0/1, Mahdi Dehghanihttps://arxiv.org/find/math/1/au:+Dehghani_M/0/1/0/all/0/1.
Abstract: The aim of this paper is to present some results concerning the $\rho_*$-orthogonality in real normed spaces and its preservation by linear operators. Among other things, we prove that if $T: X\rightarrow Y$ is a nonzero linear $(I, \rho_*)$-orthogonality preserving mapping between real normed spaces, then $$ 13|T||x|\leq |Tx|\leq 3|T||x|, x\in X $$ where $[T]:=\inf{|Tx|: x\in X, |x|=1}$. We also show that the pair $(X, \perp_{\rho_*})$ is an orthogonality space in the sense of R"{a}tz. Some characterizations of smooth spaces are given based on the $\rho_*$-orthogonality.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1705.07032