Turkish Journal of Mathematics
Abstract
We present a generalization of g-frames related to an adjointable operator $K$ on a Hilbert $C^{\ast}$-module, which we call $K$-g-frames. We obtain several characterizations of $K$-g-frames and we also give conditions under which the removal of an element from a $K$-g-frame leaves again a $K$-g-frame. In addition, we define a concept of dual, and using it we study the relation between a $K$-g-frame and a g-Bessel sequence with respect to different sequences of Hilbert $C^{\ast}$-modules.
DOI
10.3906/mat-1501-22
Keywords
Hilbert $C^{\ast}$-module, g-frame, operator, duality
First Page
453
Last Page
469
Recommended Citation
XIANG, Z, & LI, Y (2016). G-frames for operators in Hilbert $C^{\ast}$-modules. Turkish Journal of Mathematics 40 (2): 453-469. https://doi.org/10.3906/mat-1501-22
