Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximate Birkhoff-James orthogonality in the space of bounded linear
  operators   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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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn