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Santhosh Kumar","submitted_at":"2015-09-10T04:25:36Z","abstract_excerpt":"In this article, we prove the following spectral theorem for right linear normal operators (need not to be bounded) in quaternionic Hilbert spaces: Let $T$ be an unbounded right quaternionic linear normal operator in a quaternionic Hilbert space $H$ with domain $\\mathcal{D}(T)$, a right linear subspace of $H$ and fix a unit imaginary quaternion, say $m$. Then there exists a Hilbert basis $\\mathcal{N}$ of $H$ and a unique quaternionic spectral measure $F$ on the $\\sigma$- algebra of $\\mathbb C_m^{+}$ (upper half plane of the slice complex plane $\\mathbb C_m$) associated to $T$ such that \\begin{"},"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":"1509.03007","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-09-10T04:25:36Z","cross_cats_sorted":[],"title_canon_sha256":"4e8d26bd92c2691cf8d63bff4dde907a6a056e349a085661c9427dd8b7dc2fb1","abstract_canon_sha256":"aca94dbe14b4705a0c8698c84bd4f12e766ca0b9a6a4e6d734e11cf1a3067dd4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:22.783552Z","signature_b64":"i44m8TJ123VI/yrlfaikRqoUPFokRClMZyVYcFmtREKILA27IZBFkMRA4eZZl8UEYKRR8tCNn1jCCuMeksZFAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a0786eef55cafca5551b94e892eb0efe2cfc48cb60efff493e2a427313c91e8","last_reissued_at":"2026-05-18T00:31:22.783052Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:22.783052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral theorem for unbounded normal operators in quaternionic Hilbert spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"G. 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