University of MaraghehSahand Communications in Mathematical Analysis2322-580717120200101Continuous $k$-Fusion Frames in Hilbert Spaces39553673710.22130/scma.2018.83792.418ENVahidSadriDepartment of Mathematics, Shabestar Branch, Islamic Azad University Shabestar, Iran.RezaAhmadiInstitute of Fundamental Sciences, University of Tabriz, Tabriz, Iran.MohammadJafarizadehFaculty of Physic, University of Tabriz,
Tabriz, Iran.SusanNamiFaculty of Physic, University of Tabriz,
Tabriz, Iran.Journal Article20180404The study of the c$k$-fusions frames shows that the emphasis on the measure spaces introduces a new idea, although some similar properties with the discrete case are raised. Moreover, due to the nature of measure spaces, we have to use new techniques for new results. Especially, the topic of the dual of framesĀ which is important for frame applications, have been specifiedĀ completely for the continuous frames. After improving and extending the concept of fusion frames and continuous frames, in this paper we introduce continuous $k$-fusion frames in Hilbert spaces. Similarly to the c-fusion frames, dual of continuous $k$-fusion frames may not be defined, we however define the $Q$-dual of continuous $k$-fusion frames. Also some new results and the perturbation of continuous $k$-fusion frames will be presented.http://scma.maragheh.ac.ir/article_36737_f74af2ceb97b56960df44e5c8826e4a5.pdf