- Turkish Journal of Mathematics
- Vol: 40 Issue: 2
- G-frames for operators in Hilbert $C^{\ast}$-modules
G-frames for operators in Hilbert $C^{\ast}$-modules
Authors : Zhongqi Xiang, Yongming Li
Pages : 453-469
View : 6 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
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.Keywords : Hilbert $C^{ast}$-module, g-frame, operator, duality