{"paper":{"title":"Spectral decomposition of normal absolutely minimum attaining operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.FA","authors_text":"G. Ramesh, Neeru Bala","submitted_at":"2018-04-12T05:19:03Z","abstract_excerpt":"Let $T:H_1\\rightarrow H_2$ be a bounded linear operator defined between complex Hilbert spaces $H_1$ and $H_2$. We say $T$ to be \\textit{minimum attaining} if there exists a unit vector $x\\in H_1$ such that $\\|Tx\\|=m(T)$, where $m(T):=\\inf{\\{\\|Tx\\|:x\\in H_1,\\; \\|x\\|=1}\\}$ is the \\textit{minimum modulus} of $T$. We say $T$ to be \\textit{absolutely minimum attaining} ($\\mathcal{AM}$-operators in short), if for any closed subspace $M$ of $H_1$ the restriction operator $T|_M:M\\rightarrow H_2$ is minimum attaining.\n  In this paper, we give a new characterization of positive absolutely minimum attai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04321","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"}