University of MaraghehSahand Communications in Mathematical Analysis2322-580718120210201A Note on Some Results for $C$-controlled $K$-Fusion Frames in Hilbert Spaces15344657510.22130/scma.2020.123056.766ENHabibShakooryDepartment of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran.RezaAhmadiResearch Institute for Fundamental Sciences, University of Tabriz, Tabriz, Iran.NaghiBehzadiResearch Institute for Fundamental Sciences, University of Tabriz, Tabriz,
Iran.SusanNamiFaculty of Physic, University of Tabriz, Tabriz, Iran.Journal Article20200314In this manuscript, we study the relation between K-fusion frame and its local components which leads to the definition of a $C$-controlled $K$-fusion frames, also we extend a theory based on K-fusion frames on Hilbert spaces, which prepares exactly the frameworks not only to model new frames on Hilbert spaces but also for deriving robust operators. In particular, we define the analysis, synthesis and frame operator for $C$-controlled $K$-fusion frames, which even yield a reconstruction formula. Also, we define dual of $C$-controlled $K$-fusion frames and study some basic properties and perturbation of them.https://scma.maragheh.ac.ir/article_46575_1c975979396a5c2cf12c24741735cc21.pdf