Operator theory is a branch of mathematics that mainly deals with the analysis of linear operators on functional spaces, including Banach spaces and Hilbert spaces. The concept of operator theory is quite extensive and has crucial applications in many research areas, including physics, engineering, and large-scale systems. Synonyms for operator theory include functional analysis, operator algebra, linear algebra, spectral theory, and operator methods. The study of operator theory focuses on concepts such as operator equation, operator decomposition, operator factorization, and operator perturbation theory. Operator theory is essential for the development of various mathematical models and real-world applications, including quantum mechanics, signal processing, and control systems.