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Thompson proved that there exist two nxn unitary matrices U and V such that $$ e^{i X}e^{i Y}=e^{i (UXU^*+VBV^*)}. $$ In this note we consider extensions of this result to compact operators as well as to operators in an embeddable II$_1$ factor."},"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":"1107.0348","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-07-02T00:27:35Z","cross_cats_sorted":[],"title_canon_sha256":"46fa1f7faabdd118f29b02adf6f602a9b556de9481efba9cabdd9d7b01121290","abstract_canon_sha256":"b6a45fcc700467108a08079bfb00969890d9305044ca67d051c8b24df7137295"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:54.140089Z","signature_b64":"Hln0f9JSvfD1RYQsXvZwDo1mDz0xE+fcZndQuqUxmTWh6sn6H2XMukBOmRYjUL8MRnR6V4tpqInMbllriSoPCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ef05056649c07665514475ccb894937f0685d8540c32f605e5f0be59539470c","last_reissued_at":"2026-05-18T04:18:54.139599Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:54.139599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Thompson-type formulae","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alejandro Varela, Gabriel Larotonda, Jorge Antezana","submitted_at":"2011-07-02T00:27:35Z","abstract_excerpt":"Let X and Y be two nxn Hermitian matrices. 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