Operator Algebras

Operator algebras are mathematical structures used to study linear operators, which are functions that map vectors to vectors in spaces, often found in quantum mechanics and functional analysis. They provide a framework for understanding how these operators interact, including their combinations and limits. In simpler terms, they help mathematicians and physicists analyze systems where things can change over time, like the behavior of particles. Operator algebras play a crucial role in establishing the foundations of quantum theory, where they describe the properties and relationships of observable quantities.