Fuzzy atomic system and fuzzy K-frame in fuzzy Hilbert space

Prasenjit Ghosh; Jayanta Ghosh; T. K. Samanta

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arXiv · 2506.12049

Fuzzy atomic system and fuzzy K-frame in fuzzy Hilbert space

Prasenjit Ghosh·Jayanta Ghosh·T. K. Samanta

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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

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BibTeX RIS

Prasenjit Ghosh, Jayanta Ghosh, T. K. Samanta. 2025-05-27. Fuzzy atomic system and fuzzy K-frame in fuzzy Hilbert space. https://arxiv.org/abs/2506.12049

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