{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T00:43:28Z","timestamp":1759970608267,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,1,26]],"date-time":"2025-01-26T00:00:00Z","timestamp":1737849600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of China","award":["12171290","12301152","202203021222018"],"award-info":[{"award-number":["12171290","12301152","202203021222018"]}]},{"name":"Fundamental Research Program of Shanxi Province","award":["12171290","12301152","202203021222018"],"award-info":[{"award-number":["12171290","12301152","202203021222018"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Let A be a self-adjoint standard operator algebra on a real or complex Hilbert space of dimension \u22652, and let k\u2208{1,2,3}. The k-skew commutator for A,B\u2208A is defined by [A,B]1\u2217=AB\u2212BA\u2217 and [A,B]k\u2217=[A,[A,[A,B]k\u22121\u22171]1\u2217. Assume that \u03a6:A\u2192A is a map whose range contains all rank-one projections. In this paper, we prove that \u03a6 is strong k-skew-commutativity preserving, that is, [\u03a6(A),\u03a6(B)]k\u2217=[A,B]k\u2217 for all A,B\u2208A if and only if one of the following statements holds: (i) \u03a6 is either the identity map or the negative identity map whenever k\u2208{1,3}; (ii) \u03a6 is the identity map whenever k=2.<\/jats:p>","DOI":"10.3390\/axioms14020093","type":"journal-article","created":{"date-parts":[[2025,1,28]],"date-time":"2025-01-28T08:57:48Z","timestamp":1738054668000},"page":"93","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Strong k-Skew Commutativity Preserving Maps on Standard Operator Algebras"],"prefix":"10.3390","volume":"14","author":[{"given":"Ting","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Shanxi University, Taiyuan 030006, China"}]},{"given":"Xiaofei","family":"Qi","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Shanxi University, Taiyuan 030006, China"},{"name":"Key Laboratory of Complex Systems and Data Science of Ministry of Education, Shanxi University, Taiyuan 030006, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"457","DOI":"10.4153\/CMB-1994-066-4","article-title":"Strong commutativity preserving maps of semiprime ring","volume":"37","author":"Miers","year":"1994","journal-title":"Can. 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