{"paper":{"title":"A trace formula for functions of contractions and analytic operator Lipschitz functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CV","math.SP"],"primary_cat":"math.FA","authors_text":"Hagen Neidhardt, Mark Malamud, Vladimir Peller","submitted_at":"2017-05-13T02:49:43Z","abstract_excerpt":"In this note we study the problem of evaluating the trace of $f(T)-f(R)$, where $T$ and $R$ are contractions on Hilbert space with trace class difference, i.e., $T-R\\in\\boldsymbol{S}_1$ and $f$ is a function analytic in the unit disk ${\\Bbb D}$. It is well known that if $f$ is an operator Lipschitz function analytic in ${\\Bbb D}$, then $f(T)-f(R)\\in\\boldsymbol{S}_1$. The main result of the note says that there exists a function $\\boldsymbol{\\xi}$ (a spectral shift function) on the unit circle ${\\Bbb T}$ of class $L^1({\\Bbb T})$ such that the following trace formula holds: $\\operatorname{trace}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04782","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"}