{"paper":{"title":"Operator Lipschitz functions on Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Anna Tomskova, Fedor Sukochev, Jan Rozendaal","submitted_at":"2015-01-14T07:52:53Z","abstract_excerpt":"Let $X$, $Y$ be Banach spaces and let $\\mathcal{L}(X,Y)$ be the space of bounded linear operators from $X$ to $Y$. We develop the theory of double operator integrals on $\\mathcal{L}(X,Y)$ and apply this theory to obtain commutator estimates of the form $\\|f(B)S-Sf(A)\\|_{\\mathcal{L}(X,Y)}\\leq \\textrm{const} \\|BS-SA\\|_{\\mathcal{L}(X,Y)}$ for a large class of functions $f$, where $A\\in\\mathcal{L}(X)$, $B\\in \\mathcal{L}(Y)$ are scalar type operators and $S\\in \\mathcal{L}(X,Y)$. In particular, we establish this estimate for $f(t):=|t|$ and for diagonalizable operators on $X=\\ell_{p}$ and $Y=\\ell_{q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03267","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"}