Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Birkhoff-James orthogonality and applications : A survey   In the last few decades, the concept of Birkhoff-James orthogonality has been
used in several applications. In this survey article, the results known on the
necessary and sufficient conditions for Birkhoff-James orthogonality in certain
Banach spaces are mentioned. Their applications in studying the geometry of
normed spaces are given. The connections between this concept of orthogonality,
and the Gateaux derivative and the subdifferential set of the norm function are
provided. Several interesting distance formulas can be obtained using the
characterizations of Birkhoff-James orthogonality, which are also mentioned. In
the end, some new results are obtained.

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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: hep-th