Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On best approximations in Banach spaces from the perspective of
  orthogonality   We study best approximations in Banach spaces via Birkhoff-James
orthogonality of functionals. To exhibit the usefulness of Birkhoff-James
orthogonality techniques in the study of best approximation problems, some
algorithms and distance formulae are presented. As an application of our study,
we obtain some crucial inequalities, which also strengthen the classical
H\"{o}lder's inequality. The relevance of the algorithms and the inequalities
are discussed through concrete examples.

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The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess