{"paper":{"title":"Contractivity, complete contractivity and curvature inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Avijit Pal, Gadadhar Misra","submitted_at":"2014-10-28T02:27:45Z","abstract_excerpt":"For any bounded domain $\\Omega$ in $\\mathbb C^m,$ let ${\\mathrm B}_1(\\Omega)$ denote the Cowen-Douglas class of commuting $m$-tuples of bounded linear operators. For an $m$-tuple $\\boldsymbol T$ in the Cowen-Douglas class ${\\mathrm B}_1(\\Omega),$ let $N_{\\boldsymbol T}(w)$ denote the restriction of $\\boldsymbol T$ to the subspace ${\\cap_{i,j=1}^m\\ker(T_i-w_iI)(T_j-w_jI)}.$ This commuting $m$-tuple $N_{\\boldsymbol T}(w)$ of $m+1$ dimensional operators induces a homomorphism $\\rho_{_{\\!N_{\\boldsymbol T}(w)}}$ of the polynomial ring $P[z_1, ..., z_m],$ namely, $\\rho_{_{\\!N_{\\boldsymbol T}(w)}}(p)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7493","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"}