Linear maps preserving parallel matrix pairs with respect to the Ky-Fan $k$-norm
Bojan Kuzma, Chi-Kwong Li, Edward Poon, Sushil Singla · arXiv (Cornell University) · 2023
Two bounded linear operators $A$ and $B$ are parallel with respect to a norm $\|\cdot\|$ if $\|A+μB\| = \|A\| + \|B\|$ for some scalar $μ$ with $|μ| = 1$. 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.