{"paper":{"title":"Linear maps preserving Ky Fan norms and Schatten norms of tensor products of matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.FA","authors_text":"Ajda Fosner, Chi-Kwong Li, Nung-sing Sze, Zejun Huang","submitted_at":"2012-11-02T08:54:16Z","abstract_excerpt":"For a positive integer $n$, let $M_n$ be the set of $n\\times n$ complex matrices. Suppose $\\|\\cdot\\|$ is the Ky Fan $k$-norm with $1 \\le k \\le mn$ or the Schatten $p$-norm with $1 \\le p \\le \\infty$ ($p\\ne 2$) on $M_{mn}$, where $m,n\\ge 2$ are positive integers. It is shown that a linear map $\\phi: M_{mn} \\rightarrow M_{mn}$ satisfying $$\\|A\\otimes B\\| = \\|\\phi(A\\otimes B)\\| \\quad \\hbox{for all} A \\in M_m \\hbox{and} B \\in M_n$$ if and only if there are unitary $U, V \\in M_{mn}$ such that $\\phi$ has the form $A\\otimes B \\mapsto U(\\varphi_1(A) \\otimes \\varphi_2(B))V$, where $\\varphi_s(X)$ is eith"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0396","kind":"arxiv","version":2},"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"}