{"paper":{"title":"On self-adjoint operators in Krein spaces constructed by Clifford algebra Cl_2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.FA","authors_text":"Oleksii Patsiuk, Sergii Kuzhel","submitted_at":"2011-05-15T21:05:12Z","abstract_excerpt":"Let $J$ and $R$ be anti-commuting fundamental symmetries in a Hilbert space $\\mathfrak{H}$. The operators $J$ and $R$ can be interpreted as basis (generating) elements of the complex Clifford algebra ${\\mathcal C}l_2(J,R):={span}\\{I, J, R, iJR\\}$. An arbitrary non-trivial fundamental symmetry from ${\\mathcal C}l_2(J,R)$ is determined by the formula $J_{\\vec{\\alpha}}=\\alpha_{1}J+\\alpha_{2}R+\\alpha_{3}iJR$, where ${\\vec{\\alpha}}\\in\\mathbb{S}^2$.\n  Let $S$ be a symmetric operator that commutes with ${\\mathcal C}l_2(J,R)$. The purpose of this paper is to study the sets $\\Sigma_{{J_{\\vec{\\alpha}}}}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2969","kind":"arxiv","version":1},"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"}