{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:24:18Z","timestamp":1753881858913,"version":"3.41.2"},"reference-count":28,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971043"],"award-info":[{"award-number":["11971043"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971043"],"award-info":[{"award-number":["11971043"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2022,7]]},"abstract":"<jats:p> Hilbert\u2013Schmidt frame (HS-frame) has interested some mathematicians in recent years, which is more general than g-frame. This paper addresses near Riesz and Besselian properties of HS-operator sequences. We characterize HS-frame and Riesz properties of g-operator sequences using their DSI-sequences; prove that an HS-Riesz basis is an exact HS-frame while the converse is not true, and an arbitrary HS-Riesz frame contains an HS-Riesz basis; and present the connection among near HS-Riesz property, Besselian property and the kernel space dimension of synthesis operator of an HS-operator sequence. <\/jats:p>","DOI":"10.1142\/s0219691322500060","type":"journal-article","created":{"date-parts":[[2022,3,9]],"date-time":"2022-03-09T00:39:13Z","timestamp":1646786353000},"source":"Crossref","is-referenced-by-count":0,"title":["Near Riesz and Besselian Hilbert\u2013Schmidt operator sequences"],"prefix":"10.1142","volume":"20","author":[{"given":"Xiao-Li","family":"Zhang","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Beijing University of Technology, Beijing 100124, P. R. 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