Soft g-frames in soft Hilbert spaces

In this paper, we define the concept of soft $g$-frame in soft Hilbert spaces by extending the concept of soft from frame to $g$-frame. We then show some properties of the soft $g$-frames in soft Hilbert spaces. Among other results, we show that the $g$-frame operator is associated with a soft, finite, self-adjoining, reversible, and finite inverse $g$-frame and get the dual g-frames. In addition, we prove that every element in Hilbert's soft space satisfies the theorem of $g$-frame decomposition.