Local approximate symmetry of Birkhoff-James orthogonality in normed linear spaces (Q2041215)

There are two important notions of approximate orthogonality in a Banach space, one in the sense of Chmieliński ($C$-approximate orthogonality) and another one in the sense of Dragomir ($D$-approximate orthogonality). In this paper, the authors study local and global symmetry of the approximate Birkhoff-James othogonality of both types. The difference between these two types is nicely illustrated in terms of symmetry. For example, they prove that Birkhoff-James orthogonality in a finite dimensional Banach space is always $D$-approximately symmetric but not \(C\)-approximately symmetric. Further, the authors investigate \(C\)-approximate symmetry for two-dimensional polyhedral Banach spaces.