{"paper":{"title":"Numerical radius parallelism of Hilbert space operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ali Zamani, Maryam Amyari, Marzieh Mehrazin","submitted_at":"2018-10-24T15:17:32Z","abstract_excerpt":"In this paper, we introduce a new type of parallelism for bounded linear operators on a Hilbert space $\\big(\\mathscr{H}, \\langle \\cdot ,\\cdot \\rangle\\big)$ based on numerical radius. More precisely, we consider operators $T$ and $S$ which satisfy $\\omega(T + \\lambda S) = \\omega(T)+\\omega(S)$ for some complex unit $\\lambda$. We show that $T \\parallel_{\\omega} S$ if and only if there exists a sequence of unit vectors $\\{x_n\\}$ in $\\mathscr{H}$ such that \\begin{align*} \\lim_{n\\rightarrow\\infty} \\big|\\langle Tx_n, x_n\\rangle\\langle Sx_n, x_n\\rangle\\big| = \\omega(T)\\omega(S). \\end{align*} We then a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10445","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"}