{"paper":{"title":"Spectral Theorem for quaternionic normal operators: Multiplication form","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.SP","authors_text":"G. Ramesh, P. Santhosh Kumar","submitted_at":"2016-03-02T13:13:18Z","abstract_excerpt":"Let $\\mathcal{H}$ be a right quaternionic Hilbert space and let $T$ be a quaternionic normal operator with the domain $\\mathcal{D}(T) \\subset \\mathcal{H}$. Then for a fixed unit imaginary quaternion $m$, there exists a Hilbert basis $\\mathcal{N}_{m}$ of $\\mathcal{H}$, a measure space $(\\Omega, \\mu)$, a unitary operator $U \\colon \\mathcal{H} \\to L^{2}(\\Omega; \\mathbb{H}; \\mu)$ and a $\\mu$ - measurable function $\\phi \\colon \\Omega \\to \\mathbb{C}_m$ (here $\\mathbb{C}_{m} = \\{\\alpha + m \\beta; \\;\\alpha, \\beta \\in \\mathbb{R}\\}$) such that \\[ Tx = U^{*}M_{\\phi}Ux, \\; \\mbox{for all}\\; x\\in \\mathcal{D"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00697","kind":"arxiv","version":2},"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"}