{"paper":{"title":"Some generalizations of numerical radius on off-diagonal part of $2\\times 2$ operator matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Mojtaba Bakherad, Monire Hajmohamadi, Rahmatollah Lashkaripour","submitted_at":"2017-06-15T18:53:14Z","abstract_excerpt":"We generalize several inequalities involving powers of the numerical radius for off-diagonal part of $2\\times2$ operator matrices of the form $T=\\left[\\begin{array}{cc} 0&B, C&0 \\end{array}\\right]$, where $B, C$ are two operators. In particular, if $T=\\left[\\begin{array}{cc} 0&B, C&0 \\end{array}\\right]$, then we get \\begin{align*} {1\\over 2^{{3\\over2}(r-1)}}\\max\\{ \\| \\mu \\|, \\| \\eta \\| \\} \\leq w^{r}(T)\\leq \\frac{1}{2^{r+1}} \\max\\{ \\| \\mu \\|, \\| \\eta \\| \\}, \\end{align*} where $r\\geq 2$ and $ \\mu=|(C-B^{*})+i(C+B^{*})|^{r}+|(B^{*}-C)+i(C+B^{*})|^{r}$, $ \\eta=|(B-C^{*})+i(B+C^{*})|^{r}+|(C^{*}-B)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05040","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"}