{"paper":{"title":"Noncommutative functional calculate and its application","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Lvlin Luo","submitted_at":"2016-11-07T14:41:15Z","abstract_excerpt":"In this paper we construct an unitary operator $F_{xx*}$ such that $(F_{xx^{*}})^2=identity$ and $Fix(F_{xx^*})\\neq\\emptyset$. We get the unitary equivalent representations $F_{xx*}(M_{z\\psi(z)}-a)$ on $\\mathcal{L}^{2}(\\sigma(|T+a|),\\mu_{|T+a|})$ for any given $T\\in\\mathcal{B}(\\mathbb{H})$, where $\\psi(z)\\in\\mathcal{L}^{\\infty}(\\sigma(|T+a|),\\mu_{|T+a|})$, $a\\in\\rho(T)$, $F_{xx*}(f(xx^*))=f(x^*x)$, $\\mathcal{B}(\\mathbb{H})$ is the set of all bounded linear operator on complex separable Hilbert space $\\mathbb{H}$. Also, we get that if $z\\psi(z)\\in Fix(F_{xx^*})$, then $T$ has a nontrivial invar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02981","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"}