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Mathematics Subject Classification – MSC2020

46-XX

Functional analysis {For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx} 125866

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 1022

46-02

Research exposition (monographs, survey articles) pertaining to functional analysis 1516

46-03

History of functional analysis [Consider also classification numbers pertaining to Section 01-XX] 340

46-04

Software, source code, etc. for problems pertaining to functional analysis 4

46-06

Proceedings, conferences, collections, etc. pertaining to functional analysis 1134

46-08

Computational methods for problems pertaining to functional analysis 0

46-11

Research data for problems pertaining to functional analysis 0

46Axx

Topological linear spaces and related structures {For function spaces, see 46Exx} 18454

46A03

General theory of locally convex spaces 2156

46A04

Locally convex Fréchet spaces and (DF)-spaces 1445

46A08

Barrelled spaces, bornological spaces 1270

46A11

Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) 1060

46A13

Spaces defined by inductive or projective limits (LB, LF, etc.) [See also 46M40] 1065

46A16

Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) 688

46A17

Bornologies and related structures; Mackey convergence, etc. 236

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.) 734

46A20

Duality theory for topological vector spaces 1203

46A22

Theorems of Hahn-Banach type; extension and lifting of functionals and operators [See also 46M10] 780

46A25

Reflexivity and semi-reflexivity [See also 46B10] 229

46A30

Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness) 803

46A32

Spaces of linear operators; topological tensor products; approximation properties [See also 46B28, 46M05, 47L05, 47L20] 723

46A35

Summability and bases in topological vector spaces [See also 46B15] 1104

46A40

Ordered topological linear spaces, vector lattices [See also 06F20, 46B40, 46B42] 3304

46A45

Sequence spaces (including Köthe sequence spaces) [See also 46B45] 4058

46A50

Compactness in topological linear spaces; angelic spaces, etc. 694

46A55

Convex sets in topological linear spaces; Choquet theory [See also 52A07] 1850

46A61

Graded Fréchet spaces and tame operators 22

46A63

Topological invariants ((DN), (\(\Omega\)), etc.) for locally convex spaces 112

46A70

Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.) 256

46A80

Modular spaces 279

46A99

None of the above, but in this section 646

46Bxx

Normed linear spaces and Banach spaces; Banach lattices {For function spaces, see 46Exx} 23773

46B03

Isomorphic theory (including renorming) of Banach spaces 2091

46B04

Isometric theory of Banach spaces 1417

46B06

Asymptotic theory of Banach spaces [See also 52A23] 150

46B07

Local theory of Banach spaces 676

46B08

Ultraproduct techniques in Banach space theory [See also 46M07] 140

46B09

Probabilistic methods in Banach space theory [See also 60Bxx] 486

46B10

Duality and reflexivity in normed linear and Banach spaces [See also 46A25] 2103

46B15

Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces [See also 46A35, 42C15] 3221

46B20

Geometry and structure of normed linear spaces 7849

46B22

Radon-Nikodým, Kreĭn-Milman and related properties [See also 46G10] 1217

46B25

Classical Banach spaces in the general theory 2211

46B26

Nonseparable Banach spaces 460

46B28

Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20] 1327

46B40

Ordered normed spaces [See also 46A40, 46B42] 535

46B42

Banach lattices [See also 46A40, 46B40] 2039

46B45

Banach sequence spaces [See also 46A45] 1185

46B50

Compactness in Banach (or normed) spaces 434

46B70

Interpolation between normed linear spaces [See also 46M35] 1281

46B80

Nonlinear classification of Banach spaces; nonlinear quotients 97

46B85

Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science [See also 05C12, 68Rxx] 250

46B87

Lineability in functional analysis [See also 15A03] 7

46B99

None of the above, but in this section 2220

46Cxx

Inner product spaces and their generalizations, Hilbert spaces {For function spaces, see 46Exx} 4962

46C05

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) 1858

46C07

Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.) [See also 46B70, 46M35] 116

46C15

Characterizations of Hilbert spaces 456

46C20

Spaces with indefinite inner product (Kreĭn spaces, Pontryagin spaces, etc.) [See also 47B50] 841

46C50

Generalizations of inner products (semi-inner products, partial inner products, etc.) 366

46C99

None of the above, but in this section 1421

46Exx

Linear function spaces and their duals [See also 30H05, 32A38, 46F05] {For function algebras, see 46J10} 34919

46E05

Lattices of continuous, differentiable or analytic functions 465

46E10

Topological linear spaces of continuous, differentiable or analytic functions 2537

46E15

Banach spaces of continuous, differentiable or analytic functions 4230

46E20

Hilbert spaces of continuous, differentiable or analytic functions 1167

46E22

Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32] 1622

46E25

Rings and algebras of continuous, differentiable or analytic functions {For Banach function algebras, see 46J10, 46J15} 1063

46E27

Spaces of measures [See also 28A33, 46Gxx] 606

46E30

Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 11272

46E35

Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 12411

46E36

46E39

Sobolev (and similar kinds of) spaces of functions of discrete variables 182

46E40

Spaces of vector- and operator-valued functions 2760

46E50

Spaces of differentiable or holomorphic functions on infinite-dimensional spaces [See also 46G20, 46G25, 47H60] 433

46E99

None of the above, but in this section 419

46Fxx

Distributions, generalized functions, distribution spaces [See also 46T30] 8578

46F05

Topological linear spaces of test functions, distributions and ultradistributions [See also 46E10, 46E35] 2252

46F10

Operations with distributions and generalized functions 3137

46F12

Integral transforms in distribution spaces [See also 42-XX, 44-XX] 2155

46F15

Hyperfunctions, analytic functionals [See also 32A25, 32A45, 32C35, 58J15] 845

46F20

Distributions and ultradistributions as boundary values of analytic functions [See also 30D40, 30E25, 32A40] 400

46F25

Distributions on infinite-dimensional spaces [See also 58C35] 487

46F30

Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) 523

46F99

None of the above, but in this section 573

46Gxx

Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) [See also 28-XX, 46Txx] 8682

46G05

Derivatives of functions in infinite-dimensional spaces [See also 46T20, 58C20, 58C25] 2387

46G10

Vector-valued measures and integration [See also 28Bxx, 46B22] 2933

46G12

Measures and integration on abstract linear spaces [See also 28C20, 46T12] 1024

46G15

Functional analytic lifting theory [See also 28A51] 163

46G20

Infinite-dimensional holomorphy [See also 32-XX, 46E50, 46T25, 58B12, 58C10] 1525

46G25

(Spaces of) multilinear mappings, polynomials [See also 46E50, 46G20, 47H60] 737

46G99

None of the above, but in this section 317

46Hxx

Topological algebras, normed rings and algebras, Banach algebras {For group algebras, convolution algebras and measure algebras, see 43A10, 43A20} 6956

46H05

General theory of topological algebras 2668

46H10

Ideals and subalgebras 758

46H15

Representations of topological algebras 338

46H20

Structure, classification of topological algebras 819

46H25

Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) 1746

46H30

Functional calculus in topological algebras [See also 47A60] 420

46H35

Topological algebras of operators [See mainly 47Lxx] 181

46H40

Automatic continuity 368

46H70

Nonassociative topological algebras [See also 46K70, 46L70] 408

46H99

None of the above, but in this section 542

46Jxx

Commutative Banach algebras and commutative topological algebras [See also 46E25] 7326

46J05

General theory of commutative topological algebras 949

46J10

Banach algebras of continuous functions, function algebras [See also 46E25] 2506

46J15

Banach algebras of differentiable or analytic functions, \(H^p\)-spaces [See also 30H10, 32A35, 32A37, 32A38, 42B30] 3225

46J20

Ideals, maximal ideals, boundaries 1250

46J25

Representations of commutative topological algebras 196

46J30

Subalgebras of commutative topological algebras 261

46J40

Structure and classification of commutative topological algebras 200

46J45

Radical Banach algebras 80

46J99

None of the above, but in this section 242

46Kxx

Topological (rings and) algebras with an involution [See also 16W10] 1582

46K05

General theory of topological algebras with involution 556

46K10

Representations of topological algebras with involution 477

46K15

Hilbert algebras 238

46K50

Nonselfadjoint (sub)algebras in algebras with involution 83

46K70

Nonassociative topological algebras with an involution [See also 46H70, 46L70] 155

46K99

None of the above, but in this section 180

46Lxx

Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.) [See also 22D25, 47Lxx] 24224

46L05

General theory of \(C^*\)-algebras 7020

46L06

Tensor products of \(C^*\)-algebras 292

46L07

Operator spaces and completely bounded maps [See also 47L25] 956

46L08

\(C^*\)-modules 912

46L09

Free products of \(C^*\)-algebras 181

46L10

General theory of von Neumann algebras 3481

46L30

States of selfadjoint operator algebras 1057

46L35

Classifications of \(C^*\)-algebras 2002

46L36

Classification of factors 201

46L37

Subfactors and their classification 726

46L40

Automorphisms of selfadjoint operator algebras 1226

46L45

Decomposition theory for \(C^*\)-algebras 237

46L51

Noncommutative measure and integration 1584

46L52

Noncommutative function spaces 581

46L53

Noncommutative probability and statistics 2034

46L54

Free probability and free operator algebras 2056

46L55

Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 37A55] 3591

46L57

Derivations, dissipations and positive semigroups in \(C^*\)-algebras 635

46L60

Applications of selfadjoint operator algebras to physics [See also 46N50, 46N55, 47L90, 81T05, 82B10, 82C10] 1891

46L65

Quantizations, deformations for selfadjoint operator algebras 574

46L67

Quantum groups (operator algebraic aspects) 21

46L70

Nonassociative selfadjoint operator algebras [See also 46H70, 46K70] 488

46L80

\(K\)-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22] 2370

46L85

Noncommutative topology [See also 58B32, 58B34, 58J22] 1063

46L87

Noncommutative differential geometry [See also 58B32, 58B34, 58J22] 1490

46L89

Other “noncommutative” mathematics based on \(C^*\)-algebra theory [See also 58B32, 58B34, 58J22] 712

46L99

None of the above, but in this section 569

46Mxx

Methods of category theory in functional analysis [See also 18-XX] 5915

46M05

Tensor products in functional analysis [See also 46A32, 46B28, 47A80] 1713

46M07

Ultraproducts in functional analysis [See also 46B08, 46S20] 97

46M10

Projective and injective objects in functional analysis [See also 46A22] 361

46M15

Categories, functors in functional analysis {For \(K\)-theory, Ext, etc., see 19K33, 46L80, 46M18, 46M20} 539

46M18

Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.) 265

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] 1296

46M35

Abstract interpolation of topological vector spaces [See also 46B70] 1413

46M40

Inductive and projective limits in functional analysis [See also 46A13] 481

46M99

None of the above, but in this section 149

46Nxx

Miscellaneous applications of functional analysis [See also 47Nxx] 6011

46N10

Applications of functional analysis in optimization, convex analysis, mathematical programming, economics 1193

46N20

Applications of functional analysis to differential and integral equations 507

46N30

Applications of functional analysis in probability theory and statistics 712

46N40

Applications of functional analysis in numerical analysis [See also 65Jxx] 136

46N50

Applications of functional analysis in quantum physics 1808

46N55

Applications of functional analysis in statistical physics 196

46N60

Applications of functional analysis in biology and other sciences 106

46N99

None of the above, but in this section 1451

46Sxx

Other (nonclassical) types of functional analysis [See also 47Sxx] 3486

46S05

Quaternionic functional analysis 2

46S10

Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis [See also 12J25, 32P05] 1517

46S20

Nonstandard functional analysis [See also 03H05] 348

46S30

Constructive functional analysis [See also 03F60] 145

46S40

Fuzzy functional analysis [See also 03E72] 915

46S50

Functional analysis in probabilistic metric linear spaces 310

46S60

Functional analysis on superspaces (supermanifolds) or graded spaces [See also 58A50, 58C50] 284

46S99

None of the above, but in this section 33

46Txx

Nonlinear functional analysis [See also 47Hxx, 47Jxx, 58Cxx, 58Dxx] 928

46T05

Infinite-dimensional manifolds [See also 53Axx, 57N20, 58Bxx, 58Dxx] 112

46T10

Manifolds of mappings 45

46T12

Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds [See also 28Cxx, 46G12, 60-XX] 123

46T20

Continuous and differentiable maps in nonlinear functional analysis [See also 46G05] 342

46T25

Holomorphic maps in nonlinear functional analysis [See also 46G20] 75

46T30

Distributions and generalized functions on nonlinear spaces [See also 46Fxx] 99

46T99

None of the above, but in this section 151

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Mathematics Subject Classification – MSC2020

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