C*-algebras

C*-algebras are mathematical structures used in functional analysis, connecting algebraic and topological concepts. They consist of sets of bounded linear operators on a Hilbert space, which can be thought of as mathematical entities that can combine and transform vectors. C*-algebras follow specific rules, including the presence of an operation akin to multiplication and an operation related to taking adjoints (conjugates). These structures are crucial in quantum mechanics and signal processing, providing a framework for understanding various physical systems and their interactions through the lens of operator theory.