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On Fuzzy Soft Y-Class Operators in Fuzzy Soft Hilbert Spaces
Subject area: Science,Engineering and Technology · Area of research: Mathematics
DOI: https://doi.org/10.64388/IREV9I9-1715023
Abstract
This paper introduces and studies the class of fuzzy soft Y-operators in fuzzy soft Hilbert spaces, extending the classical Y-class operators introduced by Uchiyama and Yoshino (1997) to the fuzzy soft setting. Building upon the foundation of fuzzy soft normal operators established by Dawood and Jabur (2021), we define fuzzy soft f_χ-operators through the condition ↑f^χ-λf^χ+ρ^χ≤K_a^2 (f^χ-z ̂)(fⓜ-z ̂ ); for all z^χ∈C(A). We investigate fundamental properties including algebraic structure, spectral characteristics, and relationships with existing operator classes such as fuzzy soft normal, fuzzy soft self-adjoint, and fuzzy soft unitary operators. Several important theorems are proved, including a fuzzy soft Putnam-Fuglede type theorem for Y-class operators and compactness criteria. The results generalize and extend both the classical Y-operator theory and the fuzzy soft normal operator theory, providing a comprehensive framework for studying parameterized operator classes in fuzzy soft Hilbert spaces.
Keywords
Fuzzy Soft Hilbert Spaces, Y-Class Operators, Fuzzy Soft Normal Operators, Putnam-Fuglede Theorem, Spectral Theory.
How to cite this paper
@article{1715023,
author = {A. M. Nyongesa},
title = {On Fuzzy Soft Y-Class Operators in Fuzzy Soft Hilbert Spaces},
journal = {Iconic Research And Engineering Journals},
year = {2026},
volume = {9},
number = {9},
pages = {4068-4073},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/1715023.pdf},
abstract = {This paper introduces and studies the class of fuzzy soft Y-operators in fuzzy soft Hilbert spaces, extending the classical Y-class operators introduced by Uchiyama and Yoshino (1997) to the fuzzy soft setting. Building upon the foundation of fuzzy soft normal operators established by Dawood and Jabur (2021), we define fuzzy soft f_χ-operators through the condition ↑f^χ-λf^χ+ρ^χ≤K_a^2 (f^χ-z ̂)(fⓜ-z ̂ ); for all z^χ∈C(A). We investigate fundamental properties including algebraic structure, spectral characteristics, and relationships with existing operator classes such as fuzzy soft normal, fuzzy soft self-adjoint, and fuzzy soft unitary operators. Several important theorems are proved, including a fuzzy soft Putnam-Fuglede type theorem for Y-class operators and compactness criteria. The results generalize and extend both the classical Y-operator theory and the fuzzy soft normal operator theory, providing a comprehensive framework for studying parameterized operator classes in fuzzy soft Hilbert spaces.},
keywords = {Fuzzy Soft Hilbert Spaces, Y-Class Operators, Fuzzy Soft Normal Operators, Putnam-Fuglede Theorem, Spectral Theory.},
month = {March},
doi = {https://doi.org/10.64388/IREV9I9-1715023}
}