cK-frames and cK-Riesz bases in Hilbert spaces

In this paper, we prove some new results about cK-frames. Also, we introduce the concept of cK-Riesz basis and we provide a necessary and sufficient condition under which F is a cK-Riesz basis. Finally, for the closed range operator K \in B(\mathcal{H}), we prove that under some conditions, \pi_{R(K)}F is a cK-Riesz basis if and only if it has only one dual, where \pi_{R(K)} is the orthogonal projection from \mathcal{H} onto R(K), i.e., the range of K.

Keywords:

K-قاب پیوسته , K-پایه ریس پیوسته , K-دوگان پیوسته , K-قاب پیوسته ریس گونه