{"paper":{"title":"Fuglede-Putnam type theorems via the Aluthge transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"M. S. Moslehian, S. M. S. Nabavi Sales","submitted_at":"2011-12-06T15:06:08Z","abstract_excerpt":"Let $A=U|A|$ and $B=V|B|$ be the polar decompositions of $A\\in \\mathbb{B}(\\mathscr{H}_1)$ and $B\\in \\mathbb{B}(\\mathscr{H}_2)$ and let $Com(A,B)$ stand for the set of operators $X\\in\\mathbb{B}(\\mathscr{H}_2,\\mathscr{H}_1)$ such that $AX=XB$. A pair $(A,B)$ is said to have the FP-property if $Com(A,B)\\subseteqCom(A^\\ast,B^\\ast)$. Let $\\tilde{C}$ denote the Aluthge transform of a bounded linear operator $C$. We show that (i) if $A$ and $B$ are invertible and $(A,B)$ has the FP-property, then so is $(\\tilde{A},\\tilde{B})$; (ii) if $A$ and $B$ are invertible, the spectrums of both $U$ and $V$ are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1302","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"}