{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:22:12Z","timestamp":1760145732879,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,8,31]],"date-time":"2024-08-31T00:00:00Z","timestamp":1725062400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"NSF of China","doi-asserted-by":"publisher","award":["11801189"],"award-info":[{"award-number":["11801189"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper is devoted to the study of a multi-parameter subsequential version of the \u201cWiener\u2013Wintner\u201d ergodic theorem for the noncommutative Dunford\u2013Schwartz system. We establish a structure to prove \u201cWiener\u2013Wintner\u201d-type convergence over a multi-parameter subsequence class \u0394 instead of the weight class case. In our subsequence class, every term of k\u0332\u2208\u0394 is one of the three kinds of nonzero density subsequences we consider. As key ingredients, we give the maximal ergodic inequalities of multi-parameter subsequential averages and obtain a noncommutative subsequential analogue of the Banach principle. Then, by combining the critical result of the uniform convergence for a dense subset of the noncommutative Lp(M) space and the noncommutative Orlicz space, we immediately obtain the main theorem.<\/jats:p>","DOI":"10.3390\/axioms13090595","type":"journal-article","created":{"date-parts":[[2024,9,2]],"date-time":"2024-09-02T12:54:42Z","timestamp":1725281682000},"page":"595","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Noncommutative Multi-Parameter Subsequential Wiener\u2013Wintner-Type Ergodic Theorem"],"prefix":"10.3390","volume":"13","author":[{"given":"Mu","family":"Sun","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yinmei","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1090\/S0002-9904-1960-10481-8","article-title":"On the mean ergodic theorem for subsequences","volume":"66","author":"Blum","year":"1960","journal-title":"Bull. 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