{"paper":{"title":"Free bianalytic maps between spectrahedra and spectraballs in a generic setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Igor Klep, J. William Helton, Meric Augat, Scott McCullough","submitted_at":"2017-11-26T21:04:00Z","abstract_excerpt":"Given a tuple $E=(E_1,\\dots,E_g)$ of $d\\times d$ matrices, the collection of those tuples of matrices $X=(X_1,\\dots,X_g)$ (of the same size) such that $\\| \\sum E_j\\otimes X_j\\|\\le 1$ is called a spectraball $\\mathcal B_E$. Likewise, given a tuple $B=(B_1,\\dots,B_g)$ of $e\\times e$ matrices the collection of tuples of matrices $X=(X_1,\\dots,X_g)$ (of the same size) such that $I + \\sum B_j\\otimes X_j +\\sum B_j^* \\otimes X_j^*\\succeq 0$ is a free spectrahedron $\\mathcal D_B$. Assuming $E$ and $B$ are irreducible, plus an additional mild hypothesis, there is a free bianalytic map $p:\\mathcal B_E\\t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09459","kind":"arxiv","version":4},"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"}