{"paper":{"title":"Triangularizability of trace-class operators with increasing spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Roman Drnov\\v{s}ek","submitted_at":"2015-08-31T11:19:20Z","abstract_excerpt":"For any measurable set $E$ of a measure space $(X, \\mu)$, let $P_E$ be the (orthogonal) projection on the Hilbert space $L^2(X, \\mu)$ with the range $ran \\, P_E = \\{f \\in L^2(X, \\mu) : f = 0 \\ \\ a.e. \\ on \\ E^c\\}$ that is called a standard subspace of $L^2(X, \\mu)$. Let $T$ be an operator on $L^2(X, \\mu)$ having increasing spectrum relative to standard compressions, that is, for any measurable sets $E$ and $F$ with $E \\subseteq F$, the spectrum of the operator $P_E T|_{ran \\, P_E}$ is contained in the spectrum of the operator $P_F T|_{ran \\, P_F}$. In 2009, Marcoux, Mastnak and Radjavi asked w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07766","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"}