Generalized Projections Operator on Fuzzy-n-Hilbert Space
Ramla Mahdi Thgeel, Mohammed Jasim Mohammed, Hadeel Ali Shubber
Source abstract
In this study, the introduction and investigation of a new class of operator, called the generalized projection operator and the square generalized projection operator, in the framework of a Fuzzy-n-Hilbert space is considered. They are extensions of the study of projection-type operators in fuzzy inner product spaces, and they form the groundwork for the study of structural properties and mathematical behavior of these operators. The study sets out several fundamental properties, derives some key theoretical results and gives some insight into the relationships between these operators within the proposed framework. In addition, a variety of examples are given to demonstrate applicability of the definitions given and to explain the conditions for which the results given are valid. Special emphasis is placed on converse cases, explored by providing examples that illustrate that some implications are not necessarily reversible in the other direction. Furthermore, a new definition of the Fuzzy-n-Hilbert space is introduced which gives a proper mathematical framework to the operators and their properties. The results provide further insight into the generalized projection operators in the context of fuzzy functional analysis and can be used as a basis for the development of new research areas in operator theory and its possible extensions in the context of fuzzy Hilbert spaces.
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