{"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. Ramesh, P. 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{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03007","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}