{"paper":{"title":"Generators with a closure relation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Felix Schwenninger, Hans Zwart","submitted_at":"2013-09-17T14:22:44Z","abstract_excerpt":"Assume that a block operator of the form $\\left(\\begin{smallmatrix}A_{1}\\\\A_{2}\\quad 0\\end{smallmatrix}\\right)$, acting on the Banach space $X_{1}\\times X_{2}$, generates a contraction $C_{0}$-semigroup. We show that the operator $A_{S}$ defined by $A_{S}x=A_{1}\\left(\\begin{smallmatrix}x\\\\SA_{2}x\\end{smallmatrix}\\right)$ with the natural domain generates a contraction semigroup on $X_{1}$. Here, $S$ is a boundedly invertible operator for which $\\epsilon\\ide-S^{-1}$ is dissipative for some $\\epsilon>0$. With this result the existence and uniqueness of solutions of the heat equation can be deriv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4322","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"}