2020/12/15 by Chmieliński, Jacek, Khurana, Divya, Sain, Debmalya
#47L05 #52B15 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46B20 #Secondary 51F20
paper · doi:10.48550/arxiv.2012.08162
Two different notions of approximate Birkhoff-James orthogonality in nor\-med linear spaces have been introduced by Dragomir and Chmie\-liń\-ski. In the present paper we consider a global and a local approximate symmetry of the Birkhoff-James orthogonality related to each of the two definitions. We prove that the considered orthogonality is approximately symmetric in the sense of Dragomir in all finite-dimensional Banach spaces. For the other case, we prove that for finite-dimensional polyhedral Banach spaces, the approximate symmetry of the orthogonality is equivalent to some newly introduced geometric property. Our investigations complement and extend the scope of some recent results on a global approximate symmetry of the Birkhoff-James orthogonality.