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Navegando por la clasificación temática MSC 2000: 46 · Functional analysis
46 Functional analysis
  46-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
  46-01 Instructional exposition (textbooks, tutorial papers, etc.)
  46-02 Research exposition (monographs, survey articles)
  46-03 Historical
  46-04 Explicit machine computation and programs (not the theory of computation or programming)
  46-06 Proceedings, conferences, collections, etc.
  46-99 Functional analysis (not classified at a more specific level)
  46A Topological linear spaces and related structures {For function spaces, see 46Exx}
    46A03 General theory of locally convex spaces
    46A04 Locally convex Fréchet spaces and (DF)-spaces
    46A08 Barrelled spaces, bornological spaces
    46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
    46A13 Spaces defined by inductive or projective limits (LB, LF, etc.) [See also 46M40]
    46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
    46A17 Bornologies and related structures; Mackey convergence, etc.
    46A19 Other `topological'' linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than ${\bf R}$, etc.)
    46A20 Duality theory
    46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators [See also 46M10]
    46A25 Reflexivity and semi-reflexivity [See also 46B10]
    46A30 Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness)
    46A32 Spaces of linear operators; topological tensor products; approximation properties [See also 46B28, 46M05, 47L05, 47L20]
    46A35 Summability and bases [See also 46B15]
    46A40 Ordered topological linear spaces, vector lattices [See also 06F20, 46B40, 46B42]
    46A45 Sequence spaces (including Köthe sequence spaces) [See also 46B45]
    46A50 Compactness in topological linear spaces; angelic spaces, etc.
    46A55 Convex sets in topological linear spaces; Choquet theory [See also 52A07]
    46A61 Graded Fréchet spaces and tame operators
    46A63 Topological invariants ((DN), ($\Omega$), etc.)
    46A70 Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)
    46A80 Modular spaces
    46A99 None of the above, but in this section
  46B Normed linear spaces and Banach spaces; Banach lattices {For function spaces, see 46Exx}
    46B03 Isomorphic theory (including renorming) of Banach spaces
    46B04 Isometric theory of Banach spaces
    46B07 Local theory of Banach spaces
    46B08 Ultraproduct techniques in Banach space theory [See also 46M07]
    46B09 Probabilistic methods in Banach space theory [See also 60Bxx]
    46B10 Duality and reflexivity [See also 46A25]
    46B15 Summability and bases [See also 46A35]
    46B20 Geometry and structure of normed linear spaces
    46B22 Radon-Nikodym, Krein-Milman and related properties [See also 46G10]
    46B25 Classical Banach spaces in the general theory
    46B26 Nonseparable Banach spaces
    46B28 Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20]
    46B40 Ordered normed spaces [See also 46A40, 46B42]
    46B42 Banach lattices [See also 46A40, 46B40]
    46B45 Banach sequence spaces [See also 46A45]
    46B50 Compactness in Banach (or normed) spaces
    46B70 Interpolation between normed linear spaces [See also 46M35]
    46B99 None of the above, but in this section
  46C Inner product spaces and their generalizations, Hilbert spaces {For function spaces, see 46Exx}
    46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
    46C07 Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.) [See also 46B70, 46M35]
    46C15 Characterizations of Hilbert spaces
    46C20 Spaces with indefinite inner product (Krein spaces, Pontryagin spaces, etc.) [See also 47B50]
    46C50 Generalizations of inner products (semi-inner products, partial inner products, etc.)
    46C99 None of the above, but in this section
  46E Linear function spaces and their duals [See also 30H05, 32A38, 46F05] {For function algebras, see 46J10}
    46E05 Lattices of continuous, differentiable or analytic functions
    46E10 Topological linear spaces of continuous, differentiable or analytic functions
    46E15 Banach spaces of continuous, differentiable or analytic functions
    46E20 Hilbert spaces of continuous, differentiable or analytic functions
    46E22 Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32]
    46E25 Rings and algebras of continuous, differentiable or analytic functions {For Banach function algebras, see 46J10, 46J15}
    46E27 Spaces of measures [See also 28A33, 46Gxx]
    46E30 Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
    46E35 Sobolev spaces and other spaces of `smooth'' functions, embedding theorems, trace theorems
    46E39 Sobolev (and similar kinds of) spaces of functions of discrete variables
    46E40 Spaces of vector- and operator-valued functions
    46E50 Spaces of differentiable or holomorphic functions on infinite-dimensional spaces [See also 46G20, 46G25, 47H60]
    46E99 None of the above, but in this section
  46F Distributions, generalized functions, distribution spaces [See also 46T30]
    46F05 Topological linear spaces of test functions, distributions and ultradistributions [See also 46E10, 46E35]
    46F10 Operations with distributions
    46F12 Integral transforms in distribution spaces [See also 42-XX, 44-XX]
    46F15 Hyperfunctions, analytic functionals [See also 32A25, 32A45, 32C35, 58J15]
    46F20 Distributions and ultradistributions as boundary values of analytic functions [See also 30D40, 30E25, 32A40]
    46F25 Distributions on infinite-dimensional spaces [See also 58C35]
    46F30 Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
    46F99 None of the above, but in this section
  46G Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) [See also 28-XX, 46Txx]
    46G05 Derivatives [See also 46T20, 58C20, 58C25]
    46G10 Vector-valued measures and integration [See also 28Bxx, 46B22]
    46G12 Measures and integration on abstract linear spaces [See also 28C20, 46T12]
    46G15 Functional analytic lifting theory [See also 28A51]
    46G20 Infinite-dimensional holomorphy [See also 32-XX, 46E50, 46T25, 58B12, 58C10]
    46G25 (Spaces of) multilinear mappings, polynomials [See also 46E50, 46G20, 47H60]
    46G99 None of the above, but in this section
  46H Topological algebras, normed rings and algebras, Banach algebras {For group algebras, convolution algebras and measure algebras, see 43A10, 43A20}
    46H05 General theory of topological algebras
    46H10 Ideals and subalgebras
    46H15 Representations of topological algebras
    46H20 Structure, classification of topological algebras
    46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
    46H30 Functional calculus in topological algebras [See also 47A60]
    46H35 Topological algebras of operators [See mainly 47Lxx]
    46H40 Automatic continuity
    46H70 Nonassociative topological algebras [See also 46K70, 46L70]
    46H99 None of the above, but in this section
  46J Commutative Banach algebras and commutative topological [See also 46E25]
    46J05 General theory of commutative topological algebras
    46J10 Banach algebras of continuous functions, function algebras [See also 46E25]
    46J15 Banach algebras of differentiable or analytic functions, ${H}^p$-spaces [See also 30D55, 30H05, 32A35, 32A37, 32A38, 42B30]
    46J20 Ideals, maximal ideals, boundaries
    46J25 Representations of commutative topological algebras
    46J30 Subalgebras
    46J40 Structure, classification of commutative topological algebras
    46J45 Radical Banach algebras
    46J99 None of the above, but in this section
  46K Topological (rings and) algebras with an involution [See also 16W10]
    46K05 General theory of topological algebras with involution
    46K10 Representations of topological algebras with involution
    46K15 Hilbert algebras
    46K50 Nonselfadjoint (sub)algebras in algebras with involution
    46K70 Nonassociative topological algebras with an involution [See also 46H70, 46L70]
    46K99 None of the above, but in this section
  46L Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$-) algebras, etc.) [See also 22D25, 47Lxx]
    46L05 General theory of $C^*$-algebras
    46L06 Tensor products of $C^*$-algebras
    46L07 Operator spaces and completely bounded maps [See also 47L25]
    46L08 $C^*$-modules
    46L09 Free products of $C^*$-algebras
    46L10 General theory of von Neumann algebras
    46L30 States
    46L35 Classifications of $C^*$-algebras, factors
    46L37 Subfactors and their classification
    46L40 Automorphisms
    46L45 Decomposition theory for $C^*$-algebras
    46L51 Noncommutative measure and integration
    46L52 Noncommutative function spaces
    46L53 Noncommutative probability and statistics
    46L54 Free probability and free operator algebras
    46L55 Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]
    46L57 Derivations, dissipations and positive semigroups in $C^*$-algebras
    46L60 Applications of selfadjoint operator algebras to physics [See also 46N50, 46N55, 47L90, 81T05, 82B10, 82C10]
    46L65 Quantizations, deformations
    46L70 Nonassociative selfadjoint operator algebras [See also 46H70, 46K70]
    46L80 $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]
    46L85 Noncommutative topology [See also 58B32, 58B34, 58J22]
    46L87 Noncommutative differential geometry [See also 58B32, 58B34, 58J22]
    46L89 Other `noncommutative'' mathematics based on $C^*$-algebra theory [See also 58B32, 58B34, 58J22]
    46L99 None of the above, but in this section
  46M Methods of category theory in functional analysis [See also 18-XX]
    46M05 Tensor products [See also 46A32, 46B28, 47A80]
    46M07 Ultraproducts [See also 46B08, 46S20]
    46M10 Projective and injective objects [See also 46A22]
    46M15 Categories, functors {For $K$-theory, EXT, etc., see 19K33, 46L80, 46M18, 46M20}
    46M18 Homological methods (exact sequences, right inverses, lifting, etc.)
    46M20 Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.) [See also 14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx]
    46M35 Abstract interpolation of topological vector spaces [See also 46B70]
    46M40 Inductive and projective limits [See also 46A13]
    46M99 None of the above, but in this section
  46N Miscellaneous applications of functional analysis [See also 47Nxx]
    46N10 Applications in optimization, convex analysis, mathematical programming, economics
    46N20 Applications to differential and integral equations
    46N30 Applications in probability theory and statistics
    46N40 Applications in numerical analysis [See also 65Jxx]
    46N50 Applications in quantum physics
    46N55 Applications in statistical physics
    46N60 Applications in biology and other sciences
    46N99 None of the above, but in this section
  46S Other (nonclassical) types of functional analysis [See also 47Sxx]
    46S10 Functional analysis over fields other than R or C or the quaternions; non-Archimedean functional analysis [See also 12J25, 32P05]
    46S20 Nonstandard functional analysis [See also 03H05]
    46S30 Constructive functional analysis [See also 03F60]
    46S40 Fuzzy functional analysis [See also 03E72]
    46S50 Functional analysis in probabilistic metric linear spaces
    46S60 Functional analysis on superspaces (supermanifolds) or graded spaces [See also 58A50 and 58C50]
    46S99 None of the above, but in this section
  46T Nonlinear functional analysis [See also 47Hxx, 47Jxx, 58Cxx, 58Dxx]
    46T05 Infinite-dimensional manifolds [See also 53Axx, 57N20, 58Bxx, 58Dxx]
    46T10 Manifolds of mappings
    46T12 Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds [See also 28Cxx, 46G12, 60-XX]
    46T20 Continuous and differentiable maps [See also 46G05]
    46T25 Holomorphic maps [See also 46G20]
    46T30 Distributions and generalized functions on nonlinear spaces [See also 46Fxx]
    46T99 None of the above, but in this section

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