{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T03:02:06Z","timestamp":1778554926737,"version":"3.51.4"},"reference-count":27,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T00:00:00Z","timestamp":1762041600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Graduate Studies and Scientific Research at Jouf University","award":["DGSSR-2025-FC-01052"],"award-info":[{"award-number":["DGSSR-2025-FC-01052"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This manuscript introduces and investigates a new class of operators, termedn-quasi-[m,C]-symmetric operators, which generalize and extend the existing notions of [m,C]-symmetric and n-quasi-[m,C]-isometric operators. Specifically, given a conjugation C on a Hilbert space, an operator Q\u2208B(K) is said to be n-quasi-[m,C]-symmetric if it satisfies the relationQ\u2217n\u22110\u2264j\u2264m(\u22121)jmjCQm\u2212jCQjQn=0. Our study systematically explores the algebraic properties and structural characterization of n-quasi-[m,C]-symmetric operators through matrix representations, providing a deeper understanding of their internal structure. Moreover, we establish sufficient conditions under which the powers and products of such operators inherit the n-quasi-[m,C]-symmetric property. Additionally, we investigate the tensor products of n-quasi-[m,C]-symmetric operators. Finally, we identify conditions that distinguish n-quasi-[m,C]-symmetric operators from n-quasi-[m\u22121;C]-symmetric operators.<\/jats:p>","DOI":"10.3390\/sym17111836","type":"journal-article","created":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T13:47:58Z","timestamp":1762177678000},"page":"1836","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Structural Study of Generalized [m,C]-Symmetric Extension Operators"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6891-7849","authenticated-orcid":false,"given":"Sid Ahmed","family":"Ould Ahmed Mahmoud","sequence":"first","affiliation":[{"name":"Mathematics Department, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8741-1176","authenticated-orcid":false,"given":"El Moctar","family":"Ould Beiba","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences and Techniques, University of Nouakchott, P.O. Box 5026, Nouakchott, Mauritania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1439-8075","authenticated-orcid":false,"given":"Sid Ahmed","family":"Ould Beinane","sequence":"additional","affiliation":[{"name":"Mathematics Department, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-9534-9585","authenticated-orcid":false,"given":"Nura","family":"Alotaibi","sequence":"additional","affiliation":[{"name":"Mathematics Department, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1285","DOI":"10.1090\/S0002-9947-05-03742-6","article-title":"Complex symmetric operators and applications","volume":"358","author":"Garcia","year":"2006","journal-title":"Trans. Am. Math. Soc."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"353001","DOI":"10.1088\/1751-8113\/47\/35\/353001","article-title":"Mathematical and physical aspects of complex symmetric operators","volume":"47","author":"Garcia","year":"2014","journal-title":"J. Phys. A Math. 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