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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 $\\ell_1$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1804.01303","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-04-04T08:51:47Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"1a493a1b85bbfd2dff802c3b3a7c9d272fd39df470287f70b58cda9178a02896","abstract_canon_sha256":"61fa98607ad7938d44847879dfc5eb635ec51a7557ec6419f534b056a72456c1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:56.863561Z","signature_b64":"jK/OaC0/5a1/DXsq2XoiGWOEuvUMi3GwMTzT7kZOzf0abeqIp0RplTx5Qv6Hf5n4ozt5PX11fvqHbb4Ws/vuAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca1dd436842dcdefac463dc9f62516ca9f506987585e22575cacf160d2c4c541","last_reissued_at":"2026-05-18T00:18:56.863088Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:56.863088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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