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Santhosh Kumar","submitted_at":"2015-12-21T13:36:44Z","abstract_excerpt":"In this article we prove the existence of the polar decomposition for densely defined closed right linear operators in quaternionic Hilbert spaces: If $T$ is a densely defined closed right linear operator in a quaternionic Hilbert space $H$, then there exists a partial isometry $U_{0}$ such that $T = U_{0}|T|$. In fact $U_{0}$ is unique if $N(U_{0}) = N(T)$. In particular, if $H$ is separable and $U$ is a partial isometry with $T = U|T|$, then we prove that $U = U_{0}$ if and only if either $N(T) = \\{0\\}$ or $R(T)^{\\bot} = \\{0\\}$."},"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":"1512.06621","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-12-21T13:36:44Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"29afaca4fa0ed249e2c6560a29cbcbb99f00ccc517d63a41e26b45dd0b1c6f2b","abstract_canon_sha256":"71c17fae6f7ecc3f6913c7914c1c407e55580154e033fa9c528e40a688bd4bf0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:40.886368Z","signature_b64":"7BF4lNYKc6CuXCkb/GsSFc7SrgqTqDK/27uJBkAMnawAahfOfqm7M3dW4GZnUtpimZwnI29lPHLpGir73lCACA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7ce954a53fef0173281aab4c2f3183485baac324e5bb8d386d933ccb4e58659","last_reissued_at":"2026-05-18T01:06:40.885879Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:40.885879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the polar decomposition of right linear operators in quaternionic Hilbert spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.FA","authors_text":"G.Ramesh, P. 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