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Process."],"published-print":{"date-parts":[[2019,9]]},"abstract":"<jats:p> In this paper, we use a new general sequence corresponding to a [Formula: see text]-Bessel sequence [Formula: see text] to characterize that [Formula: see text] are [Formula: see text]-linear independent, [Formula: see text]-complete and a [Formula: see text]-frame. We also use [Formula: see text] and the refinement [Formula: see text] to characterize each other to be (near) exact [Formula: see text]-frames or [Formula: see text]-Riesz bases. Finally, we give several constructions and an equivalent characterization of Besselian [Formula: see text]-frames and near exact [Formula: see text]-frames. <\/jats:p>","DOI":"10.1142\/s0219691319500401","type":"journal-article","created":{"date-parts":[[2019,5,13]],"date-time":"2019-05-13T02:31:32Z","timestamp":1557714692000},"page":"1950040","source":"Crossref","is-referenced-by-count":5,"title":["Characterizations of (near) exact g-frames, g-Riesz bases, and Besselian g-frames"],"prefix":"10.1142","volume":"17","author":[{"given":"Xiangchun","family":"Xiao","sequence":"first","affiliation":[{"name":"Department of Mathematics, Xiamen University of Technology, Xiamen 361024, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yucan","family":"Zhu","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Fuzhou University, Fuzhou 350002, P. R. 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