La Classification Mathématique par matières 2000
Mathematics subject Classification 2000

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47-XX Operator theory

• 47-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 47-01 Instructional exposition (textbooks, tutorial papers, etc.)
• 47-02 Research exposition (monographs, survey articles)
• 47-03 Historical (must also be assigned at least one classification number from Section 01)
• 47-04 Explicit machine computation and programs (not the theory of computation or programming)
• 47-06 Proceedings, conferences, collections, etc.
• 47-99 Operator theory (not classified at a more specific level)
• 47Axx General theory of linear operators
• 47Bxx Special classes of linear operators
  • 47B06 Riesz operators; eigenvalue distributions; approximation numbers, s-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
  • 47B07 Operators defined by compactness properties
  • 47B10 Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20]
  • 47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)
  • 47B20 Subnormal operators, hyponormal operators, etc.
  • 47B25 Symmetric and selfadjoint operators (unbounded)
  • 47B32 Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) [See also 46E22] [Nouveau code MSC 2000]
    • Codes MSC1991 affiliés : 47A45, 47B38, 46E22
  • 47B33 Composition operators [Nouveau code MSC 2000]
    • Code MSC1991 affilié : 47B38
  • 47B34 Kernel operators [Nouveau code MSC 2000]
    • Code MSC1991 affilié : 47B38
  • 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]
  • 47B36 Jacobi (tridiagonal) operators (matrices) and generalizations [Nouveau code MSC 2000]
    • Codes MSC1991 affiliés : 39A70, 47B25, 47B37, 47B39
  • 47B37 Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
  • 47B38 Operators on function spaces (general)
  • 47B39 Difference operators [See also 39A70]
  • 47B40 Spectral operators, decomposable operators, well-bounded operators, etc.
  • 47B44 Accretive operators, dissipative operators, etc.
  • 47B47 Commutators, derivations, elementary operators, etc.
  • 47B48 Operators on Banach algebras
  • 47B49 Transformers (= operators on spaces of operators)
  • 47B50 Operators on spaces with an indefinite metric [See also 46C20]
  • 47B60 Operators on ordered spaces
  • 47B65 Positive operators and order-bounded operators
  • 47B80 Random operators [See also 60H25]
  • 47B99 None of the above, but in this section
• 47Cxx Individual linear operators as elements of algebraic systems
• 47Dxx Groups and semigroups of linear operators, their generalizations and applications
• 47E05 Ordinary differential operators [See also 34Bxx, 34Lxx]
• 47F05 Partial differential operators [See also 35Pxx, 58Jxx]
• 47Gxx Integral, integro-differential, and pseudodifferential operators [See also 58Jxx]
• 47Hxx Nonlinear operators and their properties [For global and geometric aspects, see 58-XX, especially 58Cxx]
• 47Jxx Equations and inequalities involving nonlinear operators [See also 46Txx] [For global and geometric aspects, see 58-XX]
• 47Lxx Linear spaces and algebras of operators [See also 46Lxx]
• 47Nxx Miscellaneous applications of operator theory [See also 46Nxx]
• 47Sxx Other (nonclassical) types of operator theory [See also 46Sxx]

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