C*-Algebra

A C*-algebra is a mathematical framework used to study operators on spaces that describe physical systems, especially in quantum physics. It consists of a set of complex-valued functions (or operators) equipped with operations like addition, multiplication, and a special kind of conjugate (called involution), satisfying certain rules. These algebras allow mathematicians and physicists to analyze properties of quantum states and observables abstractly, providing a rigorous foundation for understanding complex systems. Essentially, a C*-algebra captures the algebraic and topological structure necessary to model and investigate the behavior of quantum mechanical phenomena.