46Lxx Selfadjoint operator algebras (C*algebras, von Neumann (W*) algebras, etc.) [See also 22D25, 47Lxx]
 46L05 General theory of C*algebras
 46L06 Tensor products of C*algebras
 46L07 Operator spaces and completely bounded maps [See also 47L25]
 46L08 C*modules
 46L09 Free products of C*algebras
 46L10 General theory of von Neumann algebras
 46L30 States
 46L35 Classifications of C*algebras
 46L36 Classification of factors
 46L37 Subfactors and their classification
 46L40 Automorphisms
 46L45 Decomposition theory for C*algebras
 46L51 Noncommutative measure and integration
 46L52 Noncommutative function spaces

46L53 Noncommutative probability and statistics
(4)

46L54 Free probability and free operator algebras
(2)
 46L55 Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]

46L57 Derivations, dissipations and positive semigroups in C*algebras
(1)
 46L60 Applications of selfadjoint operator algebras to physics [See also 46N50, 46N55, 47L90, 81T05, 82B10, 82C10]
 46L65 Quantizations, deformations
 46L70 Nonassociative selfadjoint operator algebras [See also 46H70, 46K70]
 46L80 Ktheory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]
 46L85 Noncommutative topology [See also 58B32, 58B34, 58J22]
 46L87 Noncommutative differential geometry [See also 58B32, 58B34, 58J22]
 46L89 Other \noncommutative" mathematics based on C*algebra theory [See also 58B32, 58B34, 58J22]
 46L99 None of the above, but in this section