Mathematics Subject Classification 1991

47-XX Operator theory ( 0 Dok.)

• 47-00 General reference works (handbooks, dictionaries, bibliographies, etc.) ( 0 Dok.)
• 47-01 Instructional exposition (textbooks, tutorial papers, etc.) ( 0 Dok.)
• 47-02 Research exposition (monographs, survey articles) ( 0 Dok.)
• 47-03 Historical (must be assigned at least one classification number from Section 01) ( 0 Dok.)
• 47-04 Explicit machine computation and programs (not the theory of computation or programming) ( 0 Dok.)
• 47-06 Proceedings, conferences, collections, etc. ( 0 Dok.)
• 47Axx General theory of linear operators ( 0 Dok. )
• 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.) ( 0 Dok.)
• 47A10 Spectrum, resolvent ( 0 Dok.)
• 47A11 Local spectral properties ( 0 Dok.)
• 47A12 Numerical range ( 0 Dok.)
• 47A13 Several-variable spectral theory ( 0 Dok.)
• 47A15 Invariant subspaces ( 0 Dok.)
• 47A20 Dilations, extensions, compressions ( 0 Dok.)
• 47A25 Spectral sets ( 0 Dok.)
• 47A30 Norms (inequalities, more than one norm, etc.) ( 0 Dok.)
• 47A35 Ergodic theory, See also {28Dxx} ( 0 Dok.)
• 47A40 Scattering theory, See also {34L25, 35P25, 81Uxx} ( 0 Dok.)
• 47A45 Canonical models for contractions and nonselfadjoint operators ( 0 Dok.)
• 47A48 Operator colligations (= nodes) ( 0 Dok.)
• 47A50 Equations and inequalities involving linear operators, with vector unknowns ( 0 Dok.)
• 47A53 (Semi-) Fredholm operators; index theories, See Also { 58B10, 58G12} ( 0 Dok.)
• 47A55 Perturbation theory ( 0 Dok.)
• 47A56 Functions whose values are linear operators (operator and matrix pencils, etc.) ( 0 Dok.)
• 47A57 Operator methods in interpolation, moment and extension problems, See also {30E05, 42A70, 42A82} ( 0 Dok.)
• 47A58 Operator approximation theory ( 0 Dok.)
• 47A60 Functional calculus ( 0 Dok.)
• 47A62 Equations involving linear operators, with operator unknowns ( 0 Dok.)
• 47A63 Operator inequalities, operator means, shorted operators, etc. ( 0 Dok.)
• 47A65 Structure theory ( 0 Dok.)
• 47A66 (Non)quasitriangular, (non)quasidiagonal operators ( 0 Dok.)
• 47A67 Representation theory ( 0 Dok.)
• 47A68 Factorization theory (including Wiener-Hopf and spectral factorizations) ( 0 Dok.)
• 47A70 (Generalized) eigenfunction expansions; rigged Hilbert spaces ( 0 Dok.)
• 47A75 Eigenvalue problems, See also {49Rxx} ( 0 Dok.)
• 47A80 Tensor products of operators, See also {46M05} ( 0 Dok.)
• 47A99 None of the above but in this section ( 0 Dok.)
• 47Bxx Special classes of linear operators ( 0 Dok. )
• 47B06 Riesz operators; eigenvalue distributions; approximation numbers, $s$-numbers, Kolmogorov numbers, entropy numbers, etc. of operators ( 0 Dok.)
• 47B07 Operators defined by compactness properties ( 0 Dok.)
• 47B10 Operators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.), See also {47D50} ( 0 Dok.)
• 47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.) ( 0 Dok.)
• 47B20 Subnormal operators, hyponormal operators, etc. ( 0 Dok.)
• 47B25 Symmetric and selfadjoint operators (unbounded) ( 0 Dok.)
• 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators, See also {45P05, 47G10 for other integral operators; See also 32H10, 32M15} ( 0 Dok.)
• 47B37 Operators on special spaces (weighted shifts, operators on sequence spaces, etc.) ( 0 Dok.)
• 47B38 Operators on function spaces (including composition operators, kernel operators) ( 0 Dok.)
• 47B39 Difference operators, See also {39A70} ( 0 Dok.)
• 47B40 Spectral operators, decomposable operators, well-bounded operators, etc. ( 0 Dok.)
• 47B44 Accretive operators, dissipative operators, etc. ( 0 Dok.)
• 47B47 Commutators, derivations, elementary operators, etc. ( 0 Dok.)
• 47B48 Operators on Banach algebras ( 0 Dok.)
• 47B49 Transformers (= operators on spaces of operators) ( 0 Dok.)
• 47B50 Operators on spaces with an indefinite metric ( 0 Dok.)
• 47B60 Operators on ordered spaces ( 0 Dok.)
• 47B65 Positive operators and order-bounded operators ( 0 Dok.)
• 47B80 Random operators, See also {60H25} ( 0 Dok.)
• 47B99 None of the above but in this section ( 0 Dok.)
• 47Cxx Individual linear operators as elements of algebraic systems ( 0 Dok. )
• 47C05 Operators in algebras ( 0 Dok.)
• 47C10 Operators in *-algebras ( 0 Dok.)
• 47C15 Operators in $C$*- or von Neumann algebras ( 0 Dok.)
• 47C99 None of the above but in this section ( 0 Dok.)
• 47Dxx Algebraic systems of linear operators, See also {46Lxx} ( 0 Dok. )
• 47D03 (Semi)groups of linear operators, {For nonlinear operators, See 47H20; See also 20M20} ( 0 Dok.)
• 47D06 One-parameter semigroups and linear evolution equations ( 0 Dok.)
• 47D07 Markov semigroups, {For Markov processes, See 60Jxx} ( 0 Dok.)
• 47D09 Operator cosine functions and higher-order Cauchy problems ( 0 Dok.)
• 47D15 Linear spaces of operators, See also {46A32, 46B28} ( 0 Dok.)
• 47D20 Convex sets and cones of operators, See also {90C25, 90C31} ( 0 Dok.)
• 47D25 Operator algebras on Hilbert space ( 0 Dok.)
• 47D27 Dual operator algebras ( 0 Dok.)
• 47D30 Operator algebras on Banach spaces and other linear topological spaces ( 0 Dok.)
• 47D35 Dual spaces of operator algebras and topological groups ( 0 Dok.)
• 47D40 Algebras of unbounded operators ( 0 Dok.)
• 47D45 Applications of operator algebras to physics, See Also {46L60, 46N50, 46N55, 47N50, 47N55} ( 0 Dok.)
• 47D50 Operator ideals ( 0 Dok.)
• 47D99 None of the above but in this section ( 0 Dok.)
• 47E05 Ordinary differential operators, See also {34Bxx, 34Lxx, 58F19} ( 0 Dok.)
• 47F05 Partial differential operators, See also {35Pxx, 58G05} ( 0 Dok.)
• 47Gxx Integral, integro-differential, and pseudodifferential operators ( 0 Dok. )
• 47G10 Integral operators, See also {45P05} ( 0 Dok.)
• 47G20 Integro-differential operators, See also {45J05, 45K05} ( 0 Dok.)
• 47G30 Pseudodifferential operators, See also {35Sxx, 58G15} ( 0 Dok.)
• 47G99 None of the above but in this section ( 0 Dok.)
• 47Hxx Nonlinear operators, {For global and geometric aspects, See 58-XX, especially 58Cxx} ( 0 Dok. )
• 47H04 Set-valued operators, See also {28B20, 54C60, 58C06} ( 0 Dok.)
• 47H05 Monotone operators (with respect to duality) ( 0 Dok.)
• 47H06 Accretive operators, dissipative operators, etc. ( 0 Dok.)
• 47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces ( 0 Dok.)
• 47H09 Nonexpansive mappings, and their generalizations (ultimately compact mappings, measures of noncompactness, $A$-proper mappings, $K$-set contractions, etc.) ( 0 Dok.)
• 47H10 Fixed-point theorems, See also {54H25, 55M20, 58C30} ( 0 Dok.)
• 47H11 Degree theory, See also {55M25, 58C30} ( 0 Dok.)
• 47H12 Spectral theory of nonlinear operators, See also {58C40} ( 0 Dok.)
• 47H15 Equations involving nonlinear operators, See also {58E07 for abstract bifurcation theory} ( 0 Dok.)
• 47H17 Methods for solving equations involving nonlinear operators, See also {58C15}, {For numerical analysis, See 65J15} ( 0 Dok.)
• 47H19 Inequalities involving nonlinear operators, See Also { 49J27, 49J40, 49K27} ( 0 Dok.)
• 47H20 Semigroups of nonlinear operators and nonlinear evolution equations, See also {58D07} ( 0 Dok.)
• 47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiui, Uryson, hysteresis operators, etc.), See also {45P05} ( 0 Dok.)
• 47H40 Random operators, See also {60H25} ( 0 Dok.)
• 47H99 None of the above but in this section ( 0 Dok.)
• 47Nxx Miscellaneous applications of operator theory, See Also {46Nxx} ( 0 Dok. )
• 47N10 Applications in optimization, convex analysis, mathematical programming, economics ( 0 Dok.)
• 47N20 Applications to differential and integral equations ( 0 Dok.)
• 47N30 Applications in probability theory and statistics ( 0 Dok.)
• 47N40 Applications in numerical analysis, See also {65Jxx} ( 0 Dok.)
• 47N50 Applications in quantum physics ( 0 Dok.)
• 47N55 Applications in statistical physics ( 0 Dok.)
• 47N60 Applications in biology and other sciences ( 0 Dok.)
• 47N70 Applications in systems theory, circuits, etc. ( 0 Dok.)
• 47N99 None of the above but in this section ( 0 Dok.)
• 47Sxx Other (nonclassical) types of operator theory, See Also { 46Sxx} ( 0 Dok. )
• 47S10 Operator theory over fields other than ${R}$, ${C}$ or the quaternions; non-Archimedean operator theory ( 0 Dok.)
• 47S20 Nonstandard operator theory, See also {03H05} ( 0 Dok.)
• 47S30 Constructive operator theory, See also {03F65} ( 0 Dok.)
• 47S40 Fuzzy operator theory, See also {04A72} ( 0 Dok.)
• 47S50 Operator theory in probabilistic metric linear spaces ( 0 Dok.)
• 47S99 None of the above but in this section ( 0 Dok.)