{"paper":{"title":"The absolute values and support projections for a class of operator matrices involving idempotents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Shuaijie Wang, Xiaomei Cai, Yuan Li","submitted_at":"2018-06-14T10:07:30Z","abstract_excerpt":"Let $\\lambda\\in \\mathbb{R},$ $\\mu\\in \\mathbb{R}$ and $B$ be a linear bounded operator from a Hilbert space $\\mathcal{K}$ into another Hilbert space $\\mathcal{H}.$ In this paper, we consider the formulas of the absolute value $|Q_{\\lambda,\\mu}|,$ where $Q_{\\lambda,\\mu}$ with respect to the decomposition $\\mathcal{H}\\oplus\\mathcal{K}$ have the operator matrix\n  form $Q_{\\lambda,\\mu}:=\\left(\\begin{array}{cc}\\lambda I&B\\\\B^*&\\mu I\\end{array}\\right).$ Then the positive part and the support projection of $Q_{\\lambda,0}$ are obtained. Also, we characterize the symmetry $J$ such that a projection $E$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05443","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"}