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 $T\,: X \longrightarrow Y$ is a nonzero linear $(I, \rho_*)$-orthogonality preserving mapping between real normed spaces, then $$\frac{ 1}{ 3}\|T\|\|x\|\leq\|Tx\|\leq 3[T]\|x\|, \qquad (x\in X)$$ 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.
Categories: math.FA