46-XX Functional analysis {For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx} 137157
46-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to functional analysis 94
46-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis 1099
46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) 1092
46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) 745
46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than \(\mathbb{R}\), etc.) 760
46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators [See also 46M10] 839
46A30 Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness) 827
46A32 Spaces of linear operators; topological tensor products; approximation properties [See also 46B28, 46M05, 47L05, 47L20] 756
46A70 Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.) 269
46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces [See also 46A35, 42C15] 3469
46B28 Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20] 1507
46B85 Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science [See also 05C12, 68Rxx] 320
46Cxx Inner product spaces and their generalizations, Hilbert spaces {For function spaces, see 46Exx} 5385
46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) 2084
46C07 Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.) [See also 46B70, 46M35] 156
46C20 Spaces with indefinite inner product (Kreĭn spaces, Pontryagin spaces, etc.) [See also 47B50] 888
46Exx Linear function spaces and their duals [See also 30H05, 32A38, 46F05] {For function algebras, see 46J10} 38780
46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32] 2020
46E25 Rings and algebras of continuous, differentiable or analytic functions {For Banach function algebras, see 46J10, 46J15} 1134
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 12655
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 13792
46E36 Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces 140
46E50 Spaces of differentiable or holomorphic functions on infinite-dimensional spaces [See also 46G20, 46G25, 47H60] 465
46F05 Topological linear spaces of test functions, distributions and ultradistributions [See also 46E10, 46E35] 2428
46F20 Distributions and ultradistributions as boundary values of analytic functions [See also 30D40, 30E25, 32A40] 408
46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) [See also 28-XX, 46Txx] 9197
46Hxx Topological algebras, normed rings and algebras, Banach algebras {For group algebras, convolution algebras and measure algebras, see 43A10, 43A20} 7476
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces [See also 30H10, 32A35, 32A37, 32A38, 42B30] 3308
46Lxx Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.) [See also 22D25, 47Lxx] 26937
46L60 Applications of selfadjoint operator algebras to physics [See also 46N50, 46N55, 47L90, 81T05, 82B10, 82C10] 2003
46L80 \(K\)-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22] 2615
46L89 Other “noncommutative” mathematics based on \(C^*\)-algebra theory [See also 58B32, 58B34, 58J22] 785
46M15 Categories, functors in functional analysis {For \(K\)-theory, Ext, etc., see 19K33, 46L80, 46M18, 46M20} 590
46M18 Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.) 326
46M20 Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) [See also 14F06, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx] 1347
46N10 Applications of functional analysis in optimization, convex analysis, mathematical programming, economics 1433
46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis [See also 12J25, 32P05] 1622
46S60 Functional analysis on superspaces (supermanifolds) or graded spaces [See also 58A50, 58C50] 317
46T12 Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds [See also 28Cxx, 46G12, 60-XX] 156