zbMATH - the first resource for mathematics

Mathematics Subject Classification – MSC2010

46-XX

Functional analysis [For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx] 118898

46-00

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

46-01

Instructional exposition (textbooks, tutorial papers, etc.) 967

46-02

Research exposition (monographs, survey articles) 1418

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. 1077

46Axx

Topological linear spaces and related structures [For function spaces, see 46Exx] 17804

46A03

General theory of locally convex spaces 2113

46A04

Locally convex Fréchet spaces and (DF)-spaces 1408

46A08

Barrelled spaces, bornological spaces 1257

46A11

Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) 1049

46A13

Spaces defined by inductive or projective limits (LB, LF, etc.) [See also 46M40] 1033

46A16

Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) 654

46A17

Bornologies and related structures; Mackey convergence, etc. 228

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.) 724

46A20

Duality theory 1185

46A22

Theorems of Hahn-Banach type; extension and lifting of functionals and operators [See also 46M10] 747

46A25

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

46A30

Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness) 791

46A32

Spaces of linear operators; topological tensor products; approximation properties [See also 46B28, 46M05, 47L05, 47L20] 688

46A35

Summability and bases [See also 46B15] 1069

46A40

Ordered topological linear spaces, vector lattices [See also 06F20, 46B40, 46B42] 3195

46A45

Sequence spaces (including Köthe sequence spaces) [See also 46B45] 3830

46A50

Compactness in topological linear spaces; angelic spaces, etc. 680

46A55

Convex sets in topological linear spaces; Choquet theory [See also 52A07] 1804

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 263

46A99

None of the above, but in this section 634

46Bxx

Normed linear spaces and Banach spaces; Banach lattices [For function spaces, see 46Exx] 22367

46B03

Isomorphic theory (including renorming) of Banach spaces 1984

46B04

Isometric theory of Banach spaces 1192

46B06

Asymptotic theory of Banach spaces [See also 52A23] 108

46B07

Local theory of Banach spaces 626

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] 2049

46B15

Summability and bases [See also 46A35] 3084

46B20

Geometry and structure of normed linear spaces 7464

46B22

Radon-Nikodým, Kreĭn-Milman and related properties [See also 46G10] 1196

46B25

Classical Banach spaces in the general theory 2088

46B26

Nonseparable Banach spaces 407

46B28

Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20] 1224

46B40

Ordered normed spaces [See also 46A40, 46B42] 478

46B42

Banach lattices [See also 46A40, 46B40] 1907

46B45

Banach sequence spaces [See also 46A45] 1061

46B50

Compactness in Banach (or normed) spaces 376

46B70

Interpolation between normed linear spaces [See also 46M35] 1194

46B80

Nonlinear classification of Banach spaces; nonlinear quotients 77

46B85

Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science [See also 05C12, 68Rxx] 185

46B99

None of the above, but in this section 2176

46Cxx

Inner product spaces and their generalizations, Hilbert spaces [For function spaces, see 46Exx] 4731

46C05

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) 1741

46C07

Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.) [See also 46B70, 46M35] 102

46C15

Characterizations of Hilbert spaces 425

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.) 345

46C99

None of the above, but in this section 1393

46Exx

Linear function spaces and their duals [See also 30H05, 32A38, 46F05] [For function algebras, see 46J10] 32799

46E05

Lattices of continuous, differentiable or analytic functions 454

46E10

Topological linear spaces of continuous, differentiable or analytic functions 2455

46E15

Banach spaces of continuous, differentiable or analytic functions 4040

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] 1426

46E25

Rings and algebras of continuous, differentiable or analytic functions [For Banach function algebras, see 46J10, 46J15] 1019

46E27

Spaces of measures [See also 28A33, 46Gxx] 570

46E30

Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 10597

46E35

Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 11586

46E39

Sobolev (and similar kinds of) spaces of functions of discrete variables 166

46E40

Spaces of vector- and operator-valued functions 2623

46E50

Spaces of differentiable or holomorphic functions on infinite-dimensional spaces [See also 46G20, 46G25, 47H60] 407

46E99

None of the above, but in this section 408

46Fxx

Distributions, generalized functions, distribution spaces [See also 46T30] 8303