{"paper":{"title":"Criteria of Spectral Gap for Markov Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Feng-Yu Wang","submitted_at":"2013-05-20T08:10:53Z","abstract_excerpt":"Let $(E,\\mathcal F,\\mu)$ be a probability space, and let $P$ be a Markov operator on $L^2(\\mu)$ with $1$ a simple eigenvalue such that $\\mu P=\\mu$ (i.e. $\\mu$ is an invariant probability measure of $P$). Then $\\hat P:=\\ff 1 2 (P+P^*)$ has a spectral gap, i.e. $1$ is isolated in the spectrum of $\\hat P$, if and only if $$\\|P\\|_\\tau:=\\lim_{R\\to\\infty} \\sup_{\\mu(f^2)\\le 1}\\mu\\big(f(Pf-R)^+\\big)<1.$$ This strengthens a conjecture of Simon and H$\\phi$egh-Krohn on the spectral gap for hyperbounded operators solved recently by L. Miclo in \\cite{M}. Consequently, for a symmetric, conservative, irreduc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4460","kind":"arxiv","version":6},"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"}