On Function Lattices and Commutative von Neumann Algebras
David A. Edwards · The Quarterly Journal of Mathematics · 2002
Let A be a commutative von Neumann algebra and B a C*‐subalgebra of A that contains the identity operator. Let X, Y be the spectra of A, B respectively, and let p : X → Y be the natural map. The principal result of the paper is that B is a von Neumann algebra if and only if p is an open map. The proof leads to various other necessary and sufficient conditions for B to be a von Neumann algebra.