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arXiv · 1706.09237

Approximate Birkhoff-James orthogonality in the space of bounded linear operators

Kallol Paul·Debmalya Sain·Arpita Mal
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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 Chmieli\'nski et al. [ J. Chmieli\'nski, T. Stypula and P. W\'ojcik, \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.

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Kallol Paul, Debmalya Sain, Arpita Mal. 2017-06-28. Approximate Birkhoff-James orthogonality in the space of bounded linear operators. https://doi.org/10.1016/j.laa.2017.10.008

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