{"paper":{"title":"Root System of a Perturbation of a Selfadjoint Operator with Discrete Spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Boris Mityagin, James Adduci","submitted_at":"2011-04-05T19:04:29Z","abstract_excerpt":"We analyze the perturbations $T+B$ of a selfadjoint operator $T$ in a Hilbert space $H$ with discrete spectrum $\\{t_k \\}$, $T \\phi_k = t_k \\phi_k$, as an extension of our constructions in arXiv: 0912.2722 where $T$ was a harmonic oscillator operator. In particular, if $t_{k+1}-t_k \\geq c k^{\\alpha - 1}, \\quad \\alpha > 1/2$ and $\\| B \\phi_k \\| = o(k^{\\alpha - 1})$ then the system of root vectors of $T+B$, eventually eigenvectors of geometric multiplicity 1, is an unconditional basis in $H$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0915","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"}