I am looking for a good reference for the theorem that shows that every commutative von Neumann algebra is $*-$ isomorphic to $L^{\infty}$. Since I intend to grasp its proof perfectly.
2026-03-26 15:16:30.1774538190
Commutative von Neumann Algebras
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Takesaki, Theory of Operator Algebras volume I, Theorem III.1.18.
Murphy, C$^*$ Algebras and Operator Theory: Theorem 4.4.4
Kadison Ringrose, Theorem 9.4.1 (although one needs to work a bit to obtain the exact statement in OP)
Sakai, C$^*$ Algebras and W$^*$ Algebras, Theorem 1.18.1
Dixmier, von Neumann Algebras: Theorem I.7.3.1
Blackadar, Operator Algebras: Corollary III.1.5.18