{"paper":{"title":"The $\\lambda$-function in the space of trace class operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Antonio M. Peralta","submitted_at":"2018-04-04T08:51:47Z","abstract_excerpt":"Let $C_1(H)$ denote the space of all trace class operators on an arbitrary complex Hilbert space $H$. We prove that $C_1(H)$ satisfies the $\\lambda$-property, and we determine the form of the $\\lambda$-function of Aron and Lohman on the closed unit ball of $C_1(H)$ by showing that $$\\lambda (a) = \\frac{1 - \\|a\\|_1 + 2 \\|a\\|_{\\infty}}{2},$$ for every $a$ in ${C_1(H)}$ with $\\|a\\|_1 \\leq 1$. This is a non-commutative extension of the formula established by Aron and Lohman for $\\ell_1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01303","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"}