Fuzzy atomic system and fuzzy K-frame in fuzzy Hilbert space
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912429746683904 |
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| author | Ghosh, Prasenjit Ghosh, Jayanta Samanta, T. K. |
| author_facet | Ghosh, Prasenjit Ghosh, Jayanta Samanta, T. K. |
| contents | 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 |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12049 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fuzzy atomic system and fuzzy K-frame in fuzzy Hilbert space Ghosh, Prasenjit Ghosh, Jayanta Samanta, T. K. General Mathematics 42C15, 46C07, 46C50 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 |
| title | Fuzzy atomic system and fuzzy K-frame in fuzzy Hilbert space |
| topic | General Mathematics 42C15, 46C07, 46C50 |
| url | https://arxiv.org/abs/2506.12049 |