Some properties of weaving $K$-frames in $n$-Hilbert space

$K$-frames are more generalized than ordinary frames, particularly in terms of their weaving properties. The study of weaving $K$-frames in Hilbert space has already been explored. Given the significance of $n$-Hilbert spaces in functional analysis, it is essential to study weaving $K$-frames in $n$-Hilbert spaces. In this paper, we introduced the notion of weaving $K$-frames in $n$-Hilbert spaces and obtained some new properties for these frames using operator theory methods. First, the concept of weaving $K$-frames in $n$-Hilbert spaces is developed, and examples are given. By virtue of auxiliary operators, such as the preframe operator, analysis operator, and frame operator, some new properties and characterizations of these frames are presented, and several new methods for their construction are given. Stability and perturbation results are discussed and new inequalities are established as applications.