{"paper":{"title":"The Brown-Halmos theorem for a pair of abstract Hardy spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alexei Karlovich, Eugene Shargorodsky","submitted_at":"2018-02-23T08:25:05Z","abstract_excerpt":"Let $H[X]$ and $H[Y]$ be abstract Hardy spaces built upon Banach function spaces $X$ and $Y$ over the unit circle $\\mathbb{T}$. We prove an analogue of the Brown-Halmos theorem for Toeplitz operators $T_a$ acting from $H[X]$ to $H[Y]$ under the only assumption that the space $X$ is separable and the Riesz projection $P$ is bounded on the space $Y$. We specify our results to the case of variable Lebesgue spaces $X=L^{p(\\cdot)}$ and $Y=L^{q(\\cdot)}$ and to the case of Lorentz spaces $X=Y=L^{p,q}(w)$, $1<p<\\infty$, $1\\le q<\\infty$ with Muckenhoupt weights $w\\in A_p(\\mathbb{T})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08438","kind":"arxiv","version":2},"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"}