{"paper":{"title":"Skew-Hermitian operators in real Banach spaces of self-adjoint compact operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"B. Aminov, Vladimir Chilin","submitted_at":"2019-07-15T02:47:23Z","abstract_excerpt":"Let $\\mathcal H$ be a complex infinite-dimensional separable Hilbert space, and let $\\mathcal K(\\mathcal H)$ be the $C^*$-algebra of compact linear operators in $\\mathcal H$. Let $(E,\\|\\cdot\\|_E)$ be a symmetric sequence space. If $\\{\\mu(n,x)\\}$ are the singular values of $x\\in\\mathcal K(\\mathcal H)$, let $\\mathcal C_E=\\{x\\in\\mathcal K(\\mathcal H): \\{\\mu(n,x)\\}\\in E\\}$ with $\\|x\\|_{\\mathcal C_E}=\\|\\{\\mu(n,x)\\}\\|_E$, $x\\in\\mathcal C_E$, be the Banach ideal of compact operators generated by $E$. Let $\\mathcal C_E^h=\\{x\\in\\mathcal C_E : x=x^*\\}$ be the real Banach subspace of self-adjoint operato"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.07147","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"}