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Mathematics Subject Classification – MSC2010

46-XX

Functional analysis [For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx] 119372

46-00

General reference works (handbooks, dictionaries, bibliographies, etc.) 93

46-01

Instructional exposition (textbooks, tutorial papers, etc.) 970

46-02

Research exposition (monographs, survey articles) 1427

46-03

Historical (must also be assigned at least one classification number from Section 01) 326

46-04

Explicit machine computation and programs (not the theory of computation or programming) 3

46-06

Proceedings, conferences, collections, etc. 1082

46Axx

Topological linear spaces and related structures [For function spaces, see 46Exx] 17851

46A03

General theory of locally convex spaces 2116

46A04

Locally convex Fréchet spaces and (DF)-spaces 1409

46A08

Barrelled spaces, bornological spaces 1258

46A11

Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) 1048

46A13

Spaces defined by inductive or projective limits (LB, LF, etc.) [See also 46M40] 1037

46A16

Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) 655

46A17

Bornologies and related structures; Mackey convergence, etc. 229

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.) 723

46A20

Duality theory 1189

46A22

Theorems of Hahn-Banach type; extension and lifting of functionals and operators [See also 46M10] 751

46A25

Reflexivity and semi-reflexivity [See also 46B10] 225

46A30

Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness) 792

46A32

Spaces of linear operators; topological tensor products; approximation properties [See also 46B28, 46M05, 47L05, 47L20] 697

46A35

Summability and bases [See also 46B15] 1070

46A40

Ordered topological linear spaces, vector lattices [See also 06F20, 46B40, 46B42] 3205

46A45

Sequence spaces (including Köthe sequence spaces) [See also 46B45] 3842

46A50

Compactness in topological linear spaces; angelic spaces, etc. 678

46A55

Convex sets in topological linear spaces; Choquet theory [See also 52A07] 1808

46A61

Graded Fréchet spaces and tame operators 20

46A63

Topological invariants ((DN), ($\Omega$), etc.) 107

46A70

Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.) 250

46A80

Modular spaces 265

46A99

None of the above, but in this section 635

46Bxx

Normed linear spaces and Banach spaces; Banach lattices [For function spaces, see 46Exx] 22458

46B03

Isomorphic theory (including renorming) of Banach spaces 1996

46B04

Isometric theory of Banach spaces 1208

46B06

Asymptotic theory of Banach spaces [See also 52A23] 116

46B07

Local theory of Banach spaces 629

46B08

Ultraproduct techniques in Banach space theory [See also 46M07] 126

46B09

Probabilistic methods in Banach space theory [See also 60Bxx] 451

46B10

Duality and reflexivity [See also 46A25] 2055

46B15

Summability and bases [See also 46A35] 3093

46B20

Geometry and structure of normed linear spaces 7486

46B22

Radon-Nikodým, Kreĭn-Milman and related properties [See also 46G10] 1199

46B25

Classical Banach spaces in the general theory 2095

46B26

Nonseparable Banach spaces 411

46B28

Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20] 1233

46B40

Ordered normed spaces [See also 46A40, 46B42] 482

46B42

Banach lattices [See also 46A40, 46B40] 1915

46B45

Banach sequence spaces [See also 46A45] 1069

46B50

Compactness in Banach (or normed) spaces 380

46B70

Interpolation between normed linear spaces [See also 46M35] 1198

46B80

Nonlinear classification of Banach spaces; nonlinear quotients 80

46B85

Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science [See also 05C12, 68Rxx] 189

46B99

None of the above, but in this section 2174

46Cxx

Inner product spaces and their generalizations, Hilbert spaces [For function spaces, see 46Exx] 4747

46C05

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) 1755

46C07

Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.) [See also 46B70, 46M35] 103

46C15

Characterizations of Hilbert spaces 427

46C20

Spaces with indefinite inner product (Kreĭn spaces, Pontryagin spaces, etc.) [See also 47B50] 811

46C50

Generalizations of inner products (semi-inner products, partial inner products, etc.) 346

46C99

None of the above, but in this section 1392

46Exx

Linear function spaces and their duals [See also 30H05, 32A38, 46F05] [For function algebras, see 46J10] 32921

46E05

Lattices of continuous, differentiable or analytic functions 457

46E10

Topological linear spaces of continuous, differentiable or analytic functions 2460

46E15

Banach spaces of continuous, differentiable or analytic functions 4052

46E20

Hilbert spaces of continuous, differentiable or analytic functions 1120

46E22

Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32] 1433

46E25

Rings and algebras of continuous, differentiable or analytic functions [For Banach function algebras, see 46J10, 46J15] 1022

46E27

Spaces of measures [See also 28A33, 46Gxx] 573

46E30

Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 10631

46E35

Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 11636

46E39

Sobolev (and similar kinds of) spaces of functions of discrete variables 168

46E40

Spaces of vector- and operator-valued functions 2635

46E50

Spaces of differentiable or holomorphic functions on infinite-dimensional spaces [See also 46G20, 46G25, 47H60] 409

46E99

None of the above, but in this section 408

46Fxx

Distributions, generalized functions, distribution spaces [See also 46T30] 8325