{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,5,29]],"date-time":"2024-05-29T09:02:28Z","timestamp":1716973348916},"reference-count":18,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2020,9]]},"abstract":" The concept of [Formula: see text]-frames was recently introduced by G\u0103vruta7<\/jats:sup> in Hilbert spaces to study atomic systems with respect to a bounded linear operator. Let [Formula: see text] be a unital [Formula: see text]-algebra, [Formula: see text] be finitely or countably generated Hilbert [Formula: see text]-modules, and [Formula: see text] be adjointable operators from [Formula: see text] to [Formula: see text]. In this paper, we study a class of [Formula: see text]-bounded operators and [Formula: see text]-operator frames for [Formula: see text]. We also prove that the pseudo-inverse of [Formula: see text] exists if and only if [Formula: see text] has closed range. We extend some known results about the pseudo-inverses acting on Hilbert spaces in the context of Hilbert [Formula: see text]-modules. Further, we also present some perturbation results for [Formula: see text]-operator frames in [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0219691320500319","type":"journal-article","created":{"date-parts":[[2020,5,26]],"date-time":"2020-05-26T11:06:45Z","timestamp":1590491205000},"page":"2050031","source":"Crossref","is-referenced-by-count":3,"title":["(F,G)-operator frames for \u2112(\u210b,\ud835\udca6)"],"prefix":"10.1142","volume":"18","author":[{"given":"J.","family":"Sedghi Moghaddam","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-7563-0507","authenticated-orcid":false,"given":"A.","family":"Najati","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran"}]},{"given":"F.","family":"Ghobadzadeh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran"}]}],"member":"219","published-online":{"date-parts":[[2020,5,26]]},"reference":[{"key":"S0219691320500319BIB001","first-page":"567","volume":"38","author":"Alijani A.","year":"2012","journal-title":"Bull. 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