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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
47A11 Local spectral properties
47A12 Numerical range, numerical radius
47A13 Several-variable operator theory (spectral, Fredholm, etc.)
47A15 Invariant subspaces
47A16 Cyclic and hypercyclic vectors
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, 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
47A53 (Semi-) Fredholm operators; index theories [See also 58B15, 58J20]
47A55 Perturbation theory
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
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 49R50]
47A80 Tensor products of operators [See also 46M05]
47A99 None of the above, but in this section