The subdifferential set of the Ky Fan p-k norm is computed, yielding a characterization of best approximations and necessary and sufficient conditions for ε-Birkhoff orthogonality.
Z˘ alinescu.Convex Analysis in General Vector Spaces
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Properties of best approximations with respect to the Ky Fan $p$-$k$ norm, and the strict spectral approximant of a matrix
The subdifferential set of the Ky Fan p-k norm is computed, yielding a characterization of best approximations and necessary and sufficient conditions for ε-Birkhoff orthogonality.