{"paper":{"title":"Adjoint of sums and products of operators in Hilbert spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Zolt\\'an Sebesty\\'en, Zsigmond Tarcsay","submitted_at":"2015-07-30T08:43:59Z","abstract_excerpt":"We provide sufficient and necessary conditions guaranteeing equations $(A+B)^*=A^*+B^*$ and $(AB)^*=B^*A^*$ concerning densely defined unbounded operators $A,B$ between Hilbert spaces. We also improve the perturbation theory of selfadjoint and essentially selfadjoint operators due to Nelson, Kato, Rellich, and W\\\"ust. Our method involves the range of two-by-two matrices of the form $M_{S,T}=\\left(\\begin{array}{cc}\\!\\! I & -T\\!\\!\\\\ \\!\\! S& I\\!\\!\\end{array}\\right)$ that makes it possible to treat real and complex Hilbert spaces jointly."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08418","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"}