{"paper":{"title":"Perturbation of closed range operators and Moore-Penrose inverse","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"G. Ramesh, S. H. Kulkarni","submitted_at":"2015-10-06T11:35:22Z","abstract_excerpt":"Let $H_1,H_2$ be complex Hilbert spaces and $T:H_1\\rightarrow H_2$ be a densely defined closed operator with domain $D(T)\\subseteq H_1$ and $T^{\\dagger}$ be the Moore-Penrose inverse of $T$. Let $S:H_1\\rightarrow H_2$ be a bounded operator. In this article we focus our attention on the following questions:\n  $1.$ Under what conditions closedness of range of $T$ will imply the closedness of range of $T+S$?\n  $2.$ What is the relation between $T^{\\dagger}$ and $(T+S)^{\\dagger}$?\n  $3.$ What is the relation between $T^{\\dagger}$ and $S^{\\dagger}$?."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01534","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"}