Approximate Birkhoff-James orthogonality in the space of bounded linear operators
arXiv:1706.09237 · doi:10.1016/j.laa.2017.10.008
Abstract
There are two notions of approximate Birkhoff-James orthogonality in a normed space. We characterize both the notions of approximate Birkhoff-James orthogonality in the space of bounded linear operators defined on a normed space. A complete characterization of approximate Birkhoff-James orthogonality in the space of bounded linear operators defined on Hilbert space of any dimension is obtained which improves on the recent result by Chmieliński et al. [ J. Chmieliński, T. Stypula and P. Wójcik, \textit{Approximate orthogonality in normed spaces and its applications}, Linear Algebra and its Applications, \textbf{531} (2017), 305--317.], in which they characterized approximate Birkhoff-James orthogonality of linear operators on finite dimensional Hilbert space and also of compact operators on any Hilbert space.