Mathematical Sciences Classification System

47Axx - General theory of linear operators

  • 14
    47A05
    General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
  • 1
    47A06
    Linear relations (multivalued linear operators)
  • 3
    47A07
    Forms (bilinear, sesquilinear, multilinear)
  • 66
    47A10
    Spectrum, resolvent
  • 4
    47A11
    Local spectral properties
  • 9
    47A12
    Numerical range, numerical radius
  • 6
    47A13
    Several-variable operator theory (spectral, Fredholm, etc.)
  • 9
    47A15
    Invariant subspaces [See also 47A46]
  • 6
    47A16
    Cyclic vectors, hypercyclic and chaotic operators
  • 6
    47A20
    Dilations, extensions, compressions
  • 47A25
    Spectral sets
  • 9
    47A30
    Norms (inequalities, more than one norm, etc.)
  • 13
    47A35
    Ergodic theory [See also 28Dxx, 37Axx]
  • 18
    47A40
    Scattering theory [See also 34L25, 35P25, 37K15, 58J50, 81Uxx]
  • 3
    47A45
    Canonical models for contractions and nonselfadjoint operators
  • 2
    47A46
    Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.
  • 4
    47A48
    Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc.
  • 13
    47A50
    Equations and inequalities involving linear operators, with vector unknowns
  • 12
    47A52
    Ill-posed problems, regularization [See also 35R25, 47J06, 65F22, 65J20, 65L08, 65M30, 65R30]
  • 30
    47A53
    (Semi-) Fredholm operators; index theories [See also 58B15, 58J20]
  • 19
    47A55
    Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15]
  • 15
    47A56
    Functions whose values are linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones)
  • 16
    47A57
    Operator methods in interpolation, moment and extension problems [See also 30E05, 42A70, 42A82, 44A60]
  • 5
    47A58
    Operator approximation theory
  • 24
    47A60
    Functional calculus
  • 2
    47A62
    Equations involving linear operators, with operator unknowns
  • 9
    47A63
    Operator inequalities
  • 47A64
    Operator means, shorted operators, etc.
  • 6
    47A65
    Structure theory
  • 47A66
    Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal operators
  • 3
    47A67
    Representation theory
  • 9
    47A68
    Factorization theory (including Wiener-Hopf and spectral factorizations)
  • 11
    47A70
    (Generalized) eigenfunction expansions; rigged Hilbert spaces
  • 9
    47A75
    Eigenvalue problems [See also 47J10, 49R05]
  • 47A80
    Tensor products of operators [See also 46M05]
  • 47A99
    None of the above, but in this section

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