Operator algebras are mathematical structures that study sets of linear operators on a Hilbert space, which is a complete vector space equipped with an inner product. These algebras provide a framework for understanding various aspects of quantum mechanics and functional analysis, allowing mathematicians to explore the properties and relationships of operators. One of the key concepts in operator algebras is the C*-algebra, which is a type of algebra that is closed under certain operations, including taking adjoints and limits. Operator algebras also play a significant role in the study of von Neumann algebras, which are a special class of operator algebras that have additional properties related to measure theory and quantum physics.