{"paper":{"title":"The polarization constant of finite dimensional complex spaces is one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Daniel Galicer, Jorge Tom\\'as Rodr\\'iguez, Ver\\'onica Dimant","submitted_at":"2019-08-21T20:25:29Z","abstract_excerpt":"The polarization constant of a Banach space $X$ is defined as $$\\mathbf c(X):= \\limsup\\limits_{k\\rightarrow \\infty} \\mathbf c(k, X)^\\frac{1}{k},$$ where $\\mathbf c(k, X)$ stands for the best constant $C>0$ such that $ \\Vert \\overset{\\vee}{P} \\Vert \\leq C \\Vert P \\Vert$ for every $k$-homogeneous polynomial $P \\in \\mathcal P(^kX)$. We show that if $X$ is a finite dimensional complex space then $\\mathbf c(X)=1$. We derive some consequences of this fact regarding the convergence of analytic functions on such spaces.The result is no longer true in the real setting. Here we relate this constant with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08107","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.08107/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}