{"paper":{"title":"Preservers of Unitary Similarity Functions on Lie Products of Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Chi-Kwong Li, Jianlian Cui, Yiu-Tung Poon","submitted_at":"2014-10-22T23:47:52Z","abstract_excerpt":"Denote by $M_n$ the set of $n\\times n$ complex matrices. Let $f: M_n \\rightarrow [0,\\infty)$ be a continuous map such that $f(\\mu UAU^*)= f(A)$ for any complex unit $\\mu$, $A \\in M_n$ and unitary $U \\in M_n$, $f(X)=0$ if and only if $X=0$ and the induced map $t \\mapsto f(tX)$ is monotonic increasing on $[0,\\infty)$ for any rank 1 nilpotent $X \\in M_n$. Characterizations are given for surjective maps $\\phi$ on $M_n$ satisfying $f(AB-BA) = f(\\phi(A)\\phi(B)-\\phi(B)\\phi(A))$. The general theorem are then used to deduce results on special cases when the function is the pseudo spectrum and the pseud"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6213","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}