{"paper":{"title":"Abrahamse's Theorem for matrix-valued symbols and subnormal Toeplitz completions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"In Sung Hwang, Raul E. Curto, Woo Young Lee","submitted_at":"2013-01-29T12:03:50Z","abstract_excerpt":"This paper deals with subnormality of Toeplitz operators with matrix-valued symbols and, in particular, with an appropriate reformulation of Halmos's Problem 5: Which subnormal Toeplitz operators with matrix-valued symbols are either normal or analytic? In 1976, M. Abrahamse showed that if $\\varphi\\in L^\\infty$ is such that $\\varphi$ or $\\overline\\varphi$ is of bounded type and if $T_\\varphi$ is subnormal, then $T_\\varphi$ is either normal or analytic. In this paper we establish a matrix-valued version of Abrahamse's Theorem and then apply this result to solve the following Toeplitz completion"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6901","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"}