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The aim of this paper is to present some results concerning the$\rho_*$-orthogonality in real normed spaces and its preservation by linearoperators. Among other things, we prove that if $T\,: X \longrightarrow Y$ is anonzero linear $(I, \rho_*)$-orthogonality preserving mapping between realnormed 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 thatthe pair $(X,\perp_{\rho_*})$ is an orthogonality space in the sense ofR\"{a}tz. Some characterizations of smooth spaces are given based on the$\rho_*$-orthogonality.

Characterizations of smooth spaces by $\rho_*$-orthogonality