{"paper":{"title":"Unconditional bases of subspaces related to non-self-adjoint perturbations of self-adjoint operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.SP","authors_text":"A.A.Shkalikov, A.K.Motovilov","submitted_at":"2017-01-23T08:39:39Z","abstract_excerpt":"Assume that $T$ is a self-adjoint operator on a Hilbert space $\\mathcal{H}$ and that the spectrum of $T$ is confined in the union $\\bigcup_{j\\in J}\\Delta_j$, $J\\subseteq\\mathbb{Z}$, of segments $\\Delta_j=[\\alpha_j, \\beta_j]\\subset\\mathbb{R}$ such that $\\alpha_{j+1}>\\beta_j$ and $$ \\inf_{j} \\left(\\alpha_{j+1}-\\beta_j\\right) = d > 0. $$ If $B$ is a bounded (in general non-self-adjoint) perturbation of $T$ with $\\|B\\|=:b<d/2$ then the spectrum of the perturbed operator $A=T+B$ lies in the union $\\bigcup_{j\\in J} U_{b}(\\Delta_j)$ of the mutually disjoint closed $b$-neighborhoods $U_{b}(\\Delta_j)$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06296","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"}