{"paper":{"title":"Norm of infinite doubly stochastic matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Javad Mashreghi, Ludovick Bouthat, Rapha\\\"el Vo","submitted_at":"2026-06-23T14:09:09Z","abstract_excerpt":"In finite dimensions, every doubly stochastic matrix has the $\\ell^p$-operator norm equal to $1$ for all $1 \\le p \\le \\infty$. However, in the infinite-dimensional setting, this property may fail since the norm can be strictly smaller than $1$ when $1<p<\\infty$. In this paper, a complete characterization of infinite doubly stochastic matrices for which the norm remains equal to $1$ is obtained. More precisely, for $1<p<\\infty$, it is shown that $$ \\|D\\|_{\\ell^p(I)\\to\\ell^p(I)}=1 \\quad\\iff\\quad \\Theta(D^*D)=1, $$ where $\\Theta$ measures the maximal average mass of a finite square submatrix. Thu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24608","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.24608/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"}