##  [Von Neumann Algebra](/von-neumann-algebra) 

  ##  [Von Neumann Algebra](https://algebra.quantumdictionary.io/von-neumann-algebra-0) 

  

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Definition

A von Neumann algebra (W*-algebra) is a *‑subalgebra of B(H), the bounded operators on a Hilbert space H, that contains the identity and is closed in the weak (or strong) operator topology; equivalently, by the bicommutant theorem, it is equal to its bicommutant. Von Neumann algebras often carry a predual and admit rich projection lattices.