{"paper":{"title":"Criterion for $\\mathbb{Z}_d$--symmetry of a Spectrum of a Compact Operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.FA","authors_text":"Boris S. Mityagin","submitted_at":"2015-04-20T21:43:57Z","abstract_excerpt":"If $A$ is a compact operator in a Banach space and some power $A^q$ is nuclear we give a criterion of $\\mathbb{Z}_{d}$ -- symmetry of its spectrum $\\sigma{A}$ in terms of vanishing of the traces $\\mathop{\\mathit{Trace}} A^n$ for all $n$, $n \\geq 0$, $n \\neq 0 \\mod d$, sufficiently large."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05242","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"}