Exact K-g-Frames in Hilbert Spaces

Continuous K-g-Frames in Hilbert Spaces

“…Kframes allow us in a stable way, to reconstruct elements from the range of a linear and bounded operator in a Hilbert space. K-g-frames have been introduced in [3,11] and some properties and characterizations of K-g-frames has been obtained, for more information on K-gframes, the reader can check [11,20]. In this paper, we generalize some results in [11] and [20] to continuous version of frames.…”

Redundancy, weaving and $Q$-dual of $K$-g-frames in Hilbert spaces

“…From [20] we know that the properties between g-frames and Kg-frames are quite different, e.g., a g-Bessel sequence Λ := {Λ j ∈ L(U, V j ) : j ∈ J} is a g-frame for U, iff its synthesis operator T Λ is surjective on U (see [25]), but for K-g-frames, a g-Bessel sequence {Λ j ∈ L(U, V j ) : j ∈ J} is a K-g-frame for U, is equivalent to the synthesis operator T Λ being bounded and R(K) ⊆ R(T Λ ) (see [20]). For more information on K-g-frame and its special case K-frame, readers can refer to the [10,[18][19][20]. In this paper we will give a sufficient condition for a g-Bessel sequence to be an exact K g-frame (see Theorem 3.1).…”