W*-Algebras

W*-algebras, also known as von Neumann algebras, are a special class of mathematical structures that consist of sets of bounded linear operators acting on a Hilbert space. They are closed under certain operations like addition, multiplication, and taking adjoints, and are complete in terms of limits related to weak operator topology. These algebras are fundamental in quantum physics and functional analysis, providing a rigorous framework for studying quantum observables and states. Their structure helps mathematicians and physicists understand complex systems where infinite-dimensional spaces and operator behavior are key.