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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)
• 67
  47A10
  Spectrum, resolvent
• 4
  47A11
  Local spectral properties
• 9
  47A12
  Numerical range, numerical radius
• 6
  47A13
  Several-variable operator theory (spectral, Fredholm, etc.)
• 11
  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]
• 16
  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
• 25
  47A60
  Functional calculus
• 2
  47A62
  Equations involving linear operators, with operator unknowns
• 10
  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