In this paper, we intend to introduce the concept of c-K-gframes, which are the generalization of K-g-frames. In addition, we prove some new results on c-K-g-frames in Hilbert spaces. Moreover, we define the related operators of c-K-g frames. Then, we give necessary and sufficient conditions on c-K-g-frames to characterize them. Finally, we verify perturbation of c-K-g-frames.2010 Mathematics Subject Classification. Primary 42C15, 42C40.
We define the concept of continuous p-frames (cp-frames) for Banach spaces, generalizing discrete p-frames. We prove that under certain conditions the direct sum of a finite number of cp-frames is again a cp-frame. We obtain equivalent conditions for duals of cp-Bessel mappings and show existence and uniqueness of duals of independent cp-frames. Lastly we discuss perturbation of these frames.
In this paper we have some new results on sums of Hilbert space frames and Riesz bases. We also have a correction for some results in "S. Obeidat et al., Sums of Hilbert space frames,
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