Tusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X2420171001On symmetry of Birkhoff-James orthogonality of linear operators4284344681010.22034/aot.1703-1137ENPuja GhoshJadavpur UNiversityDebmalya SainKallol PaulJadavpur UNiversityJournal Article20170315A bounded linear operator $T$ on a normed linear space $mathbb{X}$ is said to be right symmetric (left symmetric) if $Aperp_{B} T Rightarrow T perp_B A $ ($T perp_{B} A Rightarrow A perp_B T $) for all $ A in B(mathbb{X}),$ the space of all bounded linear operators on $mathbb{X}$. Turnsek [Linear Algebra Appl., 407 (2005), 189-195] proved that if $mathbb{X}$ is a Hilbert space then $T$ is right symmetric if and only if $T$ is a scalar multiple of an isometry or coisometry. This result fails in general if the Hilbert space is replaced by a Banach space. The characterization of right and left symmetric operators on a Banach space is still open. In this paper we study the orthogonality in the sense of Birkhoff-James of bounded linear operators on $ (mathbb{R}^n, |cdot|_{infty}) $ and characterize the right symmetric and left symmetric operators on $(mathbb{R}^n,|cdot|_{infty}).$http://www.aot-math.org/article_46810_689fe803bc0e591e2c5b81af0d53b265.pdf