{"ID":23629745,"CreatedAt":"2026-09-18T07:04:54.147703138Z","UpdatedAt":"2026-09-18T07:04:54.147703138Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.20672","arxiv_id":"2609.20672","title":"Every compact operator is a commutator of compact operators","abstract":"We prove that every compact operator $T$ on a separable infinite-dimensional complex Hilbert space is a commutator of two compact operators, thereby answering a question of Pearcy and Topping. Moreover, the compact factors $A$ and $B$ can be chosen such that $[A, B] = T$ and $\\max\\{\\Vert{}A\\Vert{},\\Vert{}B\\Vert{}\\}\\leq c\\Vert{}T\\Vert{}^{1/2}$ for a universal constant $c$.","short_abstract":"We prove that every compact operator $T$ on a separable infinite-dimensional complex Hilbert space is a commutator of two compact operators, thereby answering a question of Pearcy and Topping. Moreover, the compact factors $A$ and $B$ can be chosen such that $[A, B] = T$ and $\\max\\{\\Vert{}A\\Vert{},\\Vert{}B\\Vert{}\\}\\leq...","url_abs":"https://arxiv.org/abs/2609.20672","url_pdf":"https://arxiv.org/pdf/2609.20672v1","authors":"[\"Zhichao Liu\"]","published":"2026-09-17T16:46:46Z","proceeding":"math.FA","tasks":"[\"math.FA\",\"math.OA\"]","methods":"[]","has_code":false}