{"paper":{"title":"Tests for complete $K$-spectral sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Est\\'evez, Dmitry Yakubovich, Michael A. Dritschel","submitted_at":"2015-10-28T15:39:30Z","abstract_excerpt":"Let $\\Phi$ be a family of functions analytic in some neighborhood of a complex domain $\\Omega$, and let $T$ be a Hilbert space operator whose spectrum is contained in $\\overline\\Omega$. Our typical result shows that under some extra conditions, if the closed unit disc is complete $K'$-spectral for $\\phi(T)$ for every $\\phi\\in \\Phi$, then $\\overline\\Omega$ is complete $K$-spectral for $T$ for some constant $K$. In particular, we prove that under a geometric transversality condition, the intersection of finitely many $K'$-spectral sets for $T$ is again $K$-spectral for some $K\\ge K'$. These theo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08350","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"}