47Axx General theory of linear operators
 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
 47A06 Linear relations (multivalued linear operators)
 47A07 Forms (bilinear, sesquilinear, multilinear)

47A10 Spectrum, resolvent
(1)
 47A11 Local spectral properties
 47A12 Numerical range, numerical radius
 47A13 Severalvariable operator theory (spectral, Fredholm, etc.)
 47A15 Invariant subspaces [See also 47A46]
 47A16 Cyclic vectors, hypercyclic and chaotic operators
 47A20 Dilations, extensions, compressions
 47A25 Spectral sets
 47A30 Norms (inequalities, more than one norm, etc.)
 47A35 Ergodic theory [See also 28Dxx, 37Axx]
 47A40 Scattering theory [See also 34L25, 35P25, 37K15, 58J50, 81Uxx]
 47A45 Canonical models for contractions and nonselfadjoint operators
 47A46 Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.
 47A48 Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc.
 47A50 Equations and inequalities involving linear operators, with vector unknowns

47A52 Illposed problems, regularization [See also 35R25, 47J06, 65F22, 65J20, 65L08, 65M30, 65R30]
(2)
 47A53 (Semi) Fredholm operators; index theories [See also 58B15, 58J20]
 47A55 Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15]
 47A56 Functions whose values are linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones)
 47A57 Operator methods in interpolation, moment and extension problems [See also 30E05, 42A70, 42A82, 44A60]
 47A58 Operator approximation theory

47A60 Functional calculus
(2)
 47A62 Equations involving linear operators, with operator unknowns
 47A63 Operator inequalities
 47A64 Operator means, shorted operators, etc.
 47A65 Structure theory
 47A66 Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal operators
 47A67 Representation theory
 47A68 Factorization theory (including WienerHopf and spectral factorizations)
 47A70 (Generalized) eigenfunction expansions; rigged Hilbert spaces
 47A75 Eigenvalue problems [See also 47J10, 49R05]
 47A80 Tensor products of operators [See also 46M05]
 47A99 None of the above, but in this section