{"paper":{"title":"The Spectral Picture and Joint Spectral Radius of the Generalized Spherical Aluthge Transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Chafiq Benhida, Jasang Yoon, Raul E. Curto, Sang Hoon Lee","submitted_at":"2020-06-04T21:36:13Z","abstract_excerpt":"For an arbitrary commuting $d$--tuple $\\bT$ of Hilbert space operators, we fully determine the spectral picture of the generalized spherical Aluthge transform $\\dbT$ and we prove that the spectral radius of $\\bT$ can be calculated from the norms of the iterates of $\\dbT$. \\ Let $\\bm{T} \\equiv (T_1,\\cdots,T_d)$ be a commuting $d$--tuple of bounded operators acting on an infinite dimensional separable Hilbert space, let $P:=\\sqrt{T_1^*T_1+\\cdots+T_d^*T_d}$, and let $$ \\left( \\begin{array}{c} T_1 \\\\ \\vdots \\\\ T_d \\end{array} \\right) =\n\\left( \\begin{array}{c} V_1 \\\\ \\vdots \\\\ V_d \\end{array} \\righ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.03137","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.03137/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}