{"paper":{"title":"Extremal structure of projective tensor products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Abraham Rueda Zoca, Gonzalo Mart\\'inez-Cervantes, Guillaume Grelier, Luis C. Garc\\'ia-Lirola","submitted_at":"2022-11-24T12:21:46Z","abstract_excerpt":"We prove that, given two Banach spaces $X$ and $Y$ and bounded, closed convex sets $C\\subseteq X$ and $D\\subseteq Y$, if a nonzero element $z\\in \\overline{\\mathrm{co}}(C\\otimes D)\\subseteq X\\widehat{\\otimes}_\\pi Y$ is a preserved extreme point then $z=x_0\\otimes y_0$ for some preserved extreme points $x_0\\in C$ and $y_0\\in D$, whenever $K(X,Y^*)$ separates points of $X \\widehat{\\otimes}_\\pi Y$ (in particular, whenever $X$ or $Y$ has the compact approximation property). Moreover, we prove that if $x_0\\in C$ and $y_0\\in D$ are weak-strongly exposed points then $x_0\\otimes y_0$ is weak-strongly e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.13559","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/2211.13559/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"}