{"paper":{"title":"Spectral characterization of sums of commutators I","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Nigel J. Kalton","submitted_at":"1997-09-08T00:00:00Z","abstract_excerpt":"Suppose $\\Cal J$ is a two-sided quasi-Banach ideal of compact operators on a separable infinite-dimensional Hilbert space $\\Cal H$. We show that an operator $T\\in\\Cal J$ can be expressed as finite linear combination of commutators $[A,B]$ where $A\\in\\Cal J$ and $B\\in\\Cal B(\\Cal H)$ if and only its eigenvalues $(\\lambda_n)$ (arranged in decreasing order of absolute value, repeated according to algebraic multiplicity and augmented by zeros if necessary) satisfy the condition that the diagonal operator $\\diag\\{\\frac1n(\\lambda_1+\\cdots +\\lambda_n)\\}$ is a member of $\\Cal J.$ This answers (for quas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9709209","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"}