von Neumann algebra

A von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. They were originally introduced by John von Neumann, motivated by the study of single operators, group representations, ergodic theory and quantum mechanics. His  double commutant theorem shows that the analytic definition is equivalent to a purely algebraic definition as an algebra of symmetries.
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