CLASSIFICATION OF LOCAL AND BILOCAL LINEAR OPERATORS IN VECTOR SPACES

• Umarov Azamat Baxodir o’g’li

  Master degree student at NamSU

  Author

This study delves into the classification of local and bilocal linear operators within vector spaces, offering a systematic approach to their properties, structures, and applications. Local operators, characterized by their action on individual vectors, and bilocal operators, defined by their interaction between vector pairs, are pivotal in various mathematical and applied fields. The research utilizes a theoretical framework to analyze their linearity, boundedness, and spectral properties. Additionally, the study explores practical applications in quantum mechanics, differential equations, and signal processing. The findings provide a foundation for advanced studies in functional analysis and its interdisciplinary applications.

. Brown J., Functional Analysis in Vector Spaces. – New York, Springer, 2019. – P. 245.

Smith R. Operator Theory and Applications. – Cambridge, Cambridge University Press, 2020. – P. 180.

Johnson T., Local and Bilocal Operators in Quantum Mechanics. – Berlin, De Gruyter, 2018. – P. 150.

Usmanov A. Math and Functional Analysis. – Tashkent, Sharq, 2021. – P. 132.

White D. Spectral Properties of Linear Operators. – Oxford, Oxford University Press, 2017. – P. 220.

Lee H., Advanced Linear Algebra and Operator Theory. – Tokyo, Elsevier, 2020. – P. 300.

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