Mathematics Subject Classification 1991

46-XX Functional analysis, {For manifolds modeled on topological linear spaces, See 57N20, 58Bxx} ( 0 Dok.)

• 46-00 General reference works (handbooks, dictionaries, bibliographies, etc.) ( 0 Dok.)
• 46-01 Instructional exposition (textbooks, tutorial papers, etc.) ( 0 Dok.)
• 46-02 Research exposition (monographs, survey articles) ( 0 Dok.)
• 46-03 Historical (must be assigned at least one classification number from Section 01) ( 0 Dok.)
• 46-04 Explicit machine computation and programs (not the theory of computation or programming) ( 0 Dok.)
• 46-06 Proceedings, conferences, collections, etc. ( 0 Dok.)
• 46Axx Topological linear spaces and related structures, {For function spaces, See 46Exx} ( 0 Dok. )
• 46A03 General theory of locally convex spaces ( 0 Dok.)
• 46A04 Locally convex Frechet spaces and (DF)-spaces ( 0 Dok.)
• 46A08 Barrelled spaces, bornological spaces ( 0 Dok.)
• 46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) ( 0 Dok.)
• 46A13 Spaces defined by inductive or projective limits (LB, LF, etc.), See also {46M40} ( 0 Dok.)
• 46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) ( 0 Dok.)
• 46A17 Bornologies and related structures; Mackey convergence, etc. ( 0 Dok.)
• 46A19 Other ``topological'' linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than ${R}$, etc.) ( 0 Dok.)
• 46A20 Duality theory ( 0 Dok.)
• 46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators, See also {46M10} ( 0 Dok.)
• 46A25 Reflexivity and semi-reflexivity, See also {46B10} ( 0 Dok.)
• 46A30 Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness) ( 0 Dok.)
• 46A32 Spaces of linear operators; topological tensor products; approximation properties, See also {46B28, 46M05, 47D15, 47D50} ( 0 Dok.)
• 46A35 Summability and bases, See also {46B15} ( 0 Dok.)
• 46A40 Ordered topological linear spaces, vector lattices, See also {06F20, 46B40, 46B42} ( 0 Dok.)
• 46A45 Sequence spaces (including Kothe sequence spaces), See also {46B45} ( 0 Dok.)
• 46A50 Compactness in topological linear spaces; angelic spaces, etc. ( 0 Dok.)
• 46A55 Convex sets in topological linear spaces; Choquet theory, See also {52A07} ( 0 Dok.)
• 46A70 Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.) ( 0 Dok.)
• 46A80 Modular spaces ( 0 Dok.)
• 46A99 None of the above but in this section ( 0 Dok.)
• 46Bxx Normed linear spaces and Banach spaces; Banach lattices, {For function spaces, See 46Exx} ( 0 Dok. )
• 46B03 Isomorphic theory (including renorming) of Banach spaces ( 0 Dok.)
• 46B04 Isometric theory of Banach spaces ( 0 Dok.)
• 46B07 Local theory of Banach spaces ( 0 Dok.)
• 46B08 Ultraproduct techniques in Banach space theory, See Also { 46M07} ( 0 Dok.)
• 46B09 Probabilistic methods in Banach space theory, See Also { 60Bxx} ( 0 Dok.)
• 46B10 Duality and reflexivity, See also {46A25} ( 0 Dok.)
• 46B15 Summability and bases, See also {46A35} ( 0 Dok.)
• 46B20 Geometry and structure of normed linear spaces ( 0 Dok.)
• 46B22 Radon-Nikodym, Kreuin-Milman and related properties, See also {46G10} ( 0 Dok.)
• 46B25 Classical Banach spaces in the general theory ( 0 Dok.)
• 46B26 Nonseparable Banach spaces ( 0 Dok.)
• 46B28 Spaces of operators; tensor products; approximation properties, See also {46A32, 46M05, 47D15, 47D50} ( 0 Dok.)
• 46B40 Ordered normed spaces, See also {46A40, 46B42} ( 0 Dok.)
• 46B42 Banach lattices, See also {46A40, 46B40} ( 0 Dok.)
• 46B45 Banach sequence spaces, See also {46A45} ( 0 Dok.)
• 46B70 Interpolation between normed linear spaces, See Also { 46M35} ( 0 Dok.)
• 46B99 None of the above but in this section ( 0 Dok.)
• 46Cxx Inner product spaces and their generalizations, Hilbert spaces , {For function spaces, See 46Exx} ( 0 Dok. )
• 46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) ( 0 Dok.)
• 46C15 Characterizations of Hilbert spaces ( 0 Dok.)
• 46C20 Spaces with indefinite inner product ( 0 Dok.)
• 46C50 Generalizations of inner products (semi-inner products, partial inner products, etc.) ( 0 Dok.)
• 46C99 None of the above but in this section ( 0 Dok.)
• 46Exx Linear function spaces and their duals, See also {30H05, 32E25, 46F05; for function algebras, See 46J10} ( 0 Dok. )
• 46E05 Lattices of continuous, differentiable or analytic functions ( 0 Dok.)
• 46E10 Topological linear spaces of continuous, differentiable or analytic functions ( 0 Dok.)
• 46E15 Banach spaces of continuous, differentiable or analytic functions ( 0 Dok.)
• 46E20 Hilbert spaces of continuous, differentiable or analytic functions ( 0 Dok.)
• 46E22 Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces) ( 0 Dok.)
• 46E25 Rings and algebras of continuous, differentiable or analytic functions, {For Banach function algebras, See46J10, 46J15} ( 0 Dok.)
• 46E27 Spaces of measures, See also {28A33, 46Gxx} ( 0 Dok.)
• 46E30 Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Kothe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) ( 0 Dok.)
• 46E35 Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems ( 0 Dok.)
• 46E39 Sobolev (and similar kinds of) spaces of functions of discrete variables ( 0 Dok.)
• 46E40 Spaces of vector- and operator-valued functions ( 0 Dok.)
• 46E50 Spaces of differentiable or holomorphic functions on infinite-dimensional spaces, See also {46G20} ( 0 Dok.)
• 46E99 None of the above but in this section ( 0 Dok.)
• 46Fxx Distributions, generalized functions, distribution spaces, {For distribution theory on nonlinear spaces, See 58Cxx} ( 0 Dok. )
• 46F05 Topological linear spaces of test functions, distributions and ultradistributions, See also {46E10, 46E35} ( 0 Dok.)
• 46F10 Operations with distributions ( 0 Dok.)
• 46F12 Integral transforms in distribution spaces, See Also { 42-XX, 44-XX} ( 0 Dok.)
• 46F15 Hyperfunctions, analytic functionals, See also {32A25, 32A45, 32C35, 58G07} ( 0 Dok.)
• 46F20 Distributions and ultradistributions as boundary values of analytic functions, See also {30D40, 30E25, 32A40} ( 0 Dok.)
• 46F25 Distributions on infinite-dimensional spaces, See Also { 58C35} ( 0 Dok.)
• 46F99 None of the above but in this section ( 0 Dok.)
• 46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces), See Also {28-XX} {For nonlinear functional analysis, See 47Hxx, 58-XX, especially 58Cxx} ( 0 Dok. )
• 46G05 Derivatives, See also {58C20, 58C25} ( 0 Dok.)
• 46G10 Vector-valued measures and integration, See also {28Bxx, 46B22} ( 0 Dok.)
• 46G12 Measures and integration on abstract linear spaces, See also {28C20} ( 0 Dok.)
• 46G15 Functional analytic lifting theory, See also {28A51} ( 0 Dok.)
• 46G20 Infinite-dimensional holomorphy, See also {32-XX, 46E50, 58B12, 58C10} ( 0 Dok.)
• 46G99 None of the above but in this section ( 0 Dok.)
• 46Hxx Topological algebras, normed rings and algebras, Banach algebras, {For group algebras, convolution algebras and measure algebras, See 43A10, 43A20} ( 0 Dok. )
• 46H05 General theory of topological algebras ( 0 Dok.)
• 46H10 Ideals and subalgebras ( 0 Dok.)
• 46H15 Representations of topological algebras ( 0 Dok.)
• 46H20 Structure, classification of topological algebras ( 0 Dok.)
• 46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) ( 0 Dok.)
• 46H30 Functional calculus in topological algebras, See Also { 47A60} ( 0 Dok.)
• 46H35 Topological algebras of operators [See mainly 47D30, and also 47D25, 47D50] ( 0 Dok.)
• 46H40 Automatic continuity ( 0 Dok.)
• 46H70 Nonassociative topological algebras, See also {46K70, 46L70} ( 0 Dok.)
• 46H99 None of the above but in this section ( 0 Dok.)
• 46Jxx Commutative Banach algebras and commutative topological algebras, See also {46E25} ( 0 Dok. )
• 46J05 General theory of commutative topological algebras ( 0 Dok.)
• 46J10 Banach algebras of continuous functions, function algebras, See also {46E25} ( 0 Dok.)
• 46J15 Banach algebras of differentiable or analytic functions, ${H}^p$-spaces, See also {30D55, 30H05, 32A35, 32A37, 32E25, 42B30} ( 0 Dok.)
• 46J20 Ideals, maximal ideals, boundaries ( 0 Dok.)
• 46J25 Representations of commutative topological algebras ( 0 Dok.)
• 46J30 Subalgebras ( 0 Dok.)
• 46J40 Structure, classification of commutative topological algebras ( 0 Dok.)
• 46J45 Radical Banach algebras ( 0 Dok.)
• 46J99 None of the above but in this section ( 0 Dok.)
• 46Kxx Topological (rings and) algebras with an involution, See also {16W10} ( 0 Dok. )
• 46K05 General theory of topological algebras with involution ( 0 Dok.)
• 46K10 Representations of topological algebras with involution ( 0 Dok.)
• 46K15 Hilbert algebras ( 0 Dok.)
• 46K50 Nonselfadjoint (sub)algebras in algebras with involution ( 0 Dok.)
• 46K70 Nonassociative topological algebras with an involution, See also {46H70, 46L70} ( 0 Dok.)
• 46K99 None of the above but in this section ( 0 Dok.)
• 46Lxx Selfadjoint operator algebras ($C$*-algebras, von Neumann ($W$*-) algebras, etc.), See also {22D25} ( 0 Dok. )
• 46L05 General theory of $C$*-algebras ( 0 Dok.)
• 46L10 General theory of von Neumann algebras ( 0 Dok.)
• 46L30 States ( 0 Dok.)
• 46L35 Classifications of $C^*$-algebras, factors ( 0 Dok.)
• 46L37 Subfactors and their classification ( 0 Dok.)
• 46L40 Automorphisms ( 0 Dok.)
• 46L45 Decomposition theory for $C^*$-algebras ( 0 Dok.)
• 46L50 Noncommutative measure, integration and probability ( 0 Dok.)
• 46L55 Noncommutative dynamical systems, See also {28Dxx, 54H20, 58Fxx} ( 0 Dok.)
• 46L57 Derivations, dissipations and positive semigroups in $C^*$-algebras ( 0 Dok.)
• 46L60 Applications of selfadjoint operator algebras to physics, See also {46N50, 46N55, 47D45, 81T05, 82B10, 82C10} ( 0 Dok.)
• 46L70 Nonassociative selfadjoint operator algebras, See Also {46H70, 46K70} ( 0 Dok.)
• 46L80 $K$-theory and operator algebras (including cyclic theory), See also {18F25, 19Kxx, 46M20, 55Rxx, 58G12} ( 0 Dok.)
• 46L85 Noncommutative topology, See also {58B30, 58G12} ( 0 Dok.)
• 46L87 Noncommutative differential geometry, See also {58B30, 58G12} ( 0 Dok.)
• 46L89 Other ``noncommutative'' mathematics based on $C^*$-algebra theory, See also {58B30, 58G12} ( 0 Dok.)
• 46L99 None of the above but in this section ( 0 Dok.)
• 46Mxx Methods of category theory in functional analysis, See Also { 18-XX} ( 0 Dok. )
• 46M05 Tensor products, See also {46A32, 46B28, 47A80} ( 0 Dok.)
• 46M07 Ultraproducts, See also {46B08, 46S20} ( 0 Dok.)
• 46M10 Projective and injective objects, See also {46A22} ( 0 Dok.)
• 46M15 Functors, {For $K$-theory and EXT, See 19K33, 46L80, 46M20} ( 0 Dok.)
• 46M20 Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.), See also {14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 55Rxx} ( 0 Dok.)
• 46M35 Abstract interpolation of topological vector spaces, See also {46B70} ( 0 Dok.)
• 46M40 Inductive and projective limits, See also {46A13} ( 0 Dok.)
• 46M99 None of the above but in this section ( 0 Dok.)
• 46Nxx Miscellaneous applications of functional analysis, See Also {47Nxx} ( 0 Dok. )
• 46N10 Applications in optimization, convex analysis, mathematical programming, economics ( 0 Dok.)
• 46N20 Applications to differential and integral equations ( 0 Dok.)
• 46N30 Applications in probability theory and statistics ( 0 Dok.)
• 46N40 Applications in numerical analysis, See also {65Jxx} ( 0 Dok.)
• 46N50 Applications in quantum physics ( 0 Dok.)
• 46N55 Applications in statistical physics ( 0 Dok.)
• 46N60 Applications in biology and other sciences ( 0 Dok.)
• 46N99 None of the above but in this section ( 0 Dok.)
• 46Sxx Other (nonclassical) types of functional analysis, See Also {47Sxx} ( 0 Dok. )
• 46S10 Functional analysis over fields other than ${R}$ or ${C}$ or the quaternions; non-Archimedean functional analysis, See also {12J25, 32P05} ( 0 Dok.)
• 46S20 Nonstandard functional analysis, See also {03H05} ( 0 Dok.)
• 46S30 Constructive functional analysis, See also {03F65} ( 0 Dok.)
• 46S40 Fuzzy functional analysis, See also {04A72} ( 0 Dok.)
• 46S50 Functional analysis in probabilistic metric linear spaces ( 0 Dok.)
• 46S99 None of the above but in this section ( 0 Dok.)