Abstract of a paper by Mohammad Sal Moslehian, Ali Zamani, Mahdi Dehghani
This is an announcement for the paper “Characterizations of smooth spaces by $\rho_*$-orthogonality” by Mohammad Sal Moslehian<https://arxiv.org/find/math/1/au:+Moslehian_M/0/1/0/all/0/1>, Ali Zamani<https://arxiv.org/find/math/1/au:+Zamani_A/0/1/0/all/0/1>, Mahdi Dehghani<https://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
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Bentuo Zheng (bzheng)