## 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 Several-variable 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 Ill-posed 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 Wiener-Hopf 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