46-XX Functional analysis [For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx] 116308
46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) 1042
46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) 647
46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than $\Bbb R$, etc.) 719
46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators [See also 46M10] 736
46A32 Spaces of linear operators; topological tensor products; approximation properties [See also 46B28, 46M05, 47L05, 47L20] 684
46A70 Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.) 246
46B28 Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20] 1179
46B85 Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science [See also 05C12, 68Rxx] 167
46Cxx Inner product spaces and their generalizations, Hilbert spaces [For function spaces, see 46Exx] 4623
46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) 1689
46C07 Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.) [See also 46B70, 46M35] 99
46C20 Spaces with indefinite inner product (Kreĭn spaces, Pontryagin spaces, etc.) [See also 47B50] 797
46Exx Linear function spaces and their duals [See also 30H05, 32A38, 46F05] [For function algebras, see 46J10] 32058
46E22 Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32] 1354
46E25 Rings and algebras of continuous, differentiable or analytic functions [For Banach function algebras, see 46J10, 46J15] 1007
46E30 Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 10365
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 11296
46E50 Spaces of differentiable or holomorphic functions on infinite-dimensional spaces [See also 46G20, 46G25, 47H60] 397
46F05 Topological linear spaces of test functions, distributions and ultradistributions [See also 46E10, 46E35] 2125
46F20 Distributions and ultradistributions as boundary values of analytic functions [See also 30D40, 30E25, 32A40] 390
46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) [See also 28-XX, 46Txx] 8216
46Hxx Topological algebras, normed rings and algebras, Banach algebras [For group algebras, convolution algebras and measure algebras, see 43A10, 43A20] 6513
46J15 Banach algebras of differentiable or analytic functions, $H^p$-spaces [See also 30H10, 32A35, 32A37, 32A38, 42B30] 3152
46Lxx Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$-) algebras, etc.) [See also 22D25, 47Lxx] 22022
46L60 Applications of selfadjoint operator algebras to physics [See also 46N50, 46N55, 47L90, 81T05, 82B10, 82C10] 1795
46L80 $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22] 2191
46L89 Other “noncommutative” mathematics based on $C^*$-algebra theory [See also 58B32, 58B34, 58J22] 610
46M20 Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.) [See also 14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx] 1264
46S10 Functional analysis over fields other than $\Bbb R$ or $\Bbb C$ or the quaternions; non-Archimedean functional analysis [See also 12J25, 32P05] 1424
46S60 Functional analysis on superspaces (supermanifolds) or graded spaces [See also 58A50 and 58C50] 255
46T12 Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds [See also 28Cxx, 46G12, 60-XX] 108