{"paper":{"title":"Convexity and Star-shapedness of Matricial Range","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Chi-Kwong Li, Nung-sing Sze, Pan-Shun Lau, Yiu-Tung Poon","submitted_at":"2017-10-26T06:14:21Z","abstract_excerpt":"Let ${\\bf A} = (A_1, \\dots, A_m)$ be an $m$-tuple of bounded linear operators acting on a Hilbert space ${\\cal H}$. Their joint $(p,q)$-matricial range $\\Lambda_{p,q}({\\bf A})$ is the collection of $(B_1, \\dots, B_m) \\in {\\bf M}_q^m$, where $I_p\\otimes B_j$ is a compression of $A_j$ on a $pq$-dimensional subspace. This definition covers various kinds of generalized numerical ranges for different values of $p,q,m$. In this paper, it is shown that $\\Lambda_{p,q}({\\bf A})$ is star-shaped if the dimension of $\\cal H$ is sufficiently large. If $\\dim {\\cal H}$ is infinite, we extend the definition o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09555","kind":"arxiv","version":3},"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"}