{"paper":{"title":"Double piling structure of matrix monotone functions and of matrix convex functions II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Hiroyuki Osaka, Jun Tomiyama","submitted_at":"2011-04-18T02:59:09Z","abstract_excerpt":"We continue the analysis in [H. Osaka and J. Tomiyama, Double piling structure of matrix monotone functions and of matrix convex functions, Linear and its Applications 431(2009), 1825 - 1832] in which the followings three assertions at each label $n$ are discussed: (1)$f(0) \\leq 0$ and $f$ is $n$-convex in $[0, \\alpha)$. (2)For each matrix $a$ with its spectrum in $[0, \\alpha)$ and a contraction $c$ in the matrix algebra $M_n$, $f(c^*ac) \\leq c^*f(a)c$. (3)The function $f(t)/t$ $(= g(t))$ is $n$-monotone in $(0, \\alpha)$. We know that two conditions $(2)$ and $(3)$ are equivalent and if $f$ wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3372","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"}