{"paper":{"title":"Subdifferential of the $\\mathcal{B(H,K)}$ norm, and approximate orthogonality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Krishna Kumar Gupta, Priyanka Grover, Susmita Seal","submitted_at":"2025-05-11T10:00:44Z","abstract_excerpt":"We present an expression for the right hand derivative of the $\\mathcal{B(H,K)}$ norm generalizing the result for $\\mathcal{K}=\\mathcal{H}$ in [D. J. Ke$\\check{\\mathrm{c}}$ki$\\grave{\\mathrm{c}}$, Gateaux derivative of $B(H)$ norm, Proc. Amer. Math. Soc. 133 (2005): 2061--2067]. Using this, we obtain the subdifferential of the $\\mathcal{B(H, K)}$ norm. For tuples of operators $\\mathbf{A},\\mathbf{X}\\in$ $\\mathcal{B(H, H}^d)$, we give a characterization for $\\boldsymbol 0$ to be a best approximation to the subspace $\\mathbb C^d \\mathbf{X}$, generalizing a similar result for $\\mathbb C^d \\mathbf{I"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.06925","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.06925/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}