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Linear maps preserving parallel matrix pairs with respect to the Ky-Fan $k$-norm
Published 23 Sep 2023 in math.FA | (2309.14357v1)
Abstract: Two bounded linear operators $A$ and $B$ are parallel with respect to a norm $|\cdot|$ if $|A+\mu B| = |A| + |B|$ for some scalar $\mu$ with $|\mu| = 1$. Characterization is obtained for bijective linear maps sending parallel bounded linear operators to parallel bounded linear operators with respect to the Ky-Fan $k$-norms.
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