K-g-frames in Hilbert module over locally-C^*-algebras

This paper explores the concept of K-g-frames in locally C^*-algebras, which are shown to be more general than g-frames. The authors first introduce the notion of a g-orthonormal basis and utilize it to define the g-operator, a crucial element for studying the construction of K-g-frames in locally C^*-algebras. The paper establishes a relationship between g-frames and K-g-frames and introduces the K-dual g-frame along with its properties. Finally, the authors characterize K-g-frames through two other related concepts.