{"paper":{"title":"Completely bounded norms of right module maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Richard M. Timoney, Rupert H. Levene","submitted_at":"2011-02-21T15:39:05Z","abstract_excerpt":"It is well-known that if T is a D_m-D_n bimodule map on the m by n complex matrices, then T is a Schur multiplier and $\\|T\\|_{cb}=\\|T\\|$. If n=2 and T is merely assumed to be a right D_2-module map, then we show that $\\|T\\|_{cb}=\\|T\\|$. However, this property fails if m>1 and n>2. For m>1 and n=3,4 or $n\\geq m^2$, we give examples of maps T attaining the supremum C(m,n)=\\sup \\|T\\|_{cb} taken over the contractive, right D_n-module maps on M_{m,n}, we show that C(m,m^2)=\\sqrt{m} and succeed in finding sharp results for C(m,n) in certain other cases. As a consequence, if H is an infinite-dimensio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4255","kind":"arxiv","version":3},"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"}