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. (2017) [4], 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.
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