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In this note we prove a variant of Tingley's problem by showing that every surjective isometry $\\Delta : S(B(H_1)^+)\\to S(B(H_2)^+)$ or (respectively, $\\Delta : S(K(H_3)^+)\\to S(K(H_4)^+)$) admits a unique extension to a surjective complex linear isometry from $B(H_1)$ onto $B(H_2))$ (respectively, from $K(H_3)$ onto $B(H_4)$). This provides a positive answer to a c"},"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":"1711.05652","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-15T16:29:29Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"755131926932e89f6383f2f5d4a75207417ed1aeb018ffacb3fbe6e6a18111ba","abstract_canon_sha256":"dff1d81647d647d45a780078d42e1d6886a729e1d5eea47d220a74c92fdadef4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:48.508256Z","signature_b64":"G6d3Fd4Dgu10XnxGFFFwoHGbjnJGFHvnN+9wx1zwmKpClZqkWA1z5aOhV8XvaOwn4TOmknzl9+U+0L2auZYbDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17666015c7ec039796e8b007e8c62191d358a190a6b1c901025fcef4c31f7441","last_reissued_at":"2026-05-17T23:56:48.507836Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:48.507836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the unit sphere of positive operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Antonio M. Peralta","submitted_at":"2017-11-15T16:29:29Z","abstract_excerpt":"Given a C$^*$-algebra $A$, let $S(A^+)$ denote the set of those positive elements in the unit sphere of $A$. Let $H_1$, $H_2,$ $H_3$ and $H_4$ be complex Hilbert spaces, where $H_3$ and $H_4$ are infinite-dimensional and separable. In this note we prove a variant of Tingley's problem by showing that every surjective isometry $\\Delta : S(B(H_1)^+)\\to S(B(H_2)^+)$ or (respectively, $\\Delta : S(K(H_3)^+)\\to S(K(H_4)^+)$) admits a unique extension to a surjective complex linear isometry from $B(H_1)$ onto $B(H_2))$ (respectively, from $K(H_3)$ onto $B(H_4)$). 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