Abstract
Hilbert \(C^*\)-modules generalize Hilbert spaces which allow the inner product to take values in a \(C^*\)-algebra rather than in the field of real or complex numbers. A frame is a more flexible substitute for a basis, and it allows us to represent a vector as linear combinations of frame elements in multiple ways. Frank and Larson, in 2002 introduced the notion of frames in Hilbert \(C^*\)-modules. Here, we present a thorough discussion on frames in Hilbert \(C^*\)-modules. We discuss different types of frames, such as K-frames, controlled frames, fusion frames and weaving frames with examples. We also define weaving K-frames and explain this new concept with examples.
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