Banach spaces, as mathematical structures equipped with norms, have found profound applications in various branches of mathematics, but their utility extends far beyond pure mathematics. In recent years, the application of Banach spaces in quantum mechanics has gained significant attention, offering new insights and perspectives into the fundamental principles of quantum theory. This paper explores the applications of Banach spaces in quantum mechanics, elucidating their role in the description of quantum states, observables, and dynamics. Furthermore, it discusses the potential implications of Banach space techniques in addressing foundational issues and advancing quantum technologies. Through a comprehensive review of relevant literature and examples, this paper aims to provide a deeper understanding of the interplay between Banach spaces and quantum mechanics, highlighting both existing applications and future directions.