{"paper":{"title":"Some applications of almost analytic extensions to operator bounds in trace ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.FA","authors_text":"Fritz Gesztesy, Roger Nichols","submitted_at":"2015-02-04T02:25:49Z","abstract_excerpt":"Using the Davies-Helffer-Sj\\\"ostrand functional calculus based on almost analytic extensions, we address the following problem: Given self-adjoint operators $S_j$, $j=1,2$, in $\\mathcal{H}$, and functions $f$ in an appropriate class, for instance, $f \\in C_0^{\\infty}(\\mathbb{R})$, how to control the norm $\\|f(S_2) - f(S_1)\\|_{\\mathcal{B}(\\mathcal{H})}$ in terms of the norm of the difference of resolvents, $\\|(S_2 - z_0 I_{\\mathcal{H}})^{-1} - (S_2 - z_0 I_{\\mathcal{H}})^{-1}\\|_{\\mathcal{B}(\\mathcal{H})}$, for some $z_0 \\in \\mathbb{C}\\backslash\\mathbb{R}$. We are particularly interested in the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01078","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"}