von Neumann algebra

A von Neumann algebra is a mathematical structure used in functional analysis and quantum mechanics. It consists of a set of operators (mathematical objects acting on spaces of functions) that are closed under certain operations, like taking limits and forming adjoints. This means if you combine operators in specific ways, you stay within the same set. These algebras help describe quantum systems, where observables (like position or momentum) can be represented as operators. They also provide a framework for understanding the mathematical foundation of quantum theory in a rigorous way.