Fuzzy atomic system and fuzzy K-frame in fuzzy Hilbert space (2506.12049v1)

Abstract: Atomic system in fuzzy Hilbert space is introduced and the existence of the fuzzy atomic systems for a strongly fuzzy bounded linear operator is studied. The notion of a K-frame in fuzzy Hilbert space is presented and some of their characterizations are given. We will see that fuzzy frame operator of a fuzzy K-frame in fuzzy Hilbert space is invertible under some sufficient condition and validates this by giving some examples. Fuzzy K-frame property in fuzzy Hilbert space preserve by a strongly fuzzy bounded linear operator is established. We will describe stability condition of fuzzy K-frame in fuzzy Hilbert space under some perturbations. We construct new types of fuzzy K-frame using fuzzy K-frame in fuzzy Hilbert space. Further, it is seen that scalar combinations and product of two fuzzy K-frames is also a fuzzy K-frame in fuzzy Hilbert space