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MSC2020 · 47Axx

General theory of linear operators

General theory of linear operators

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Counts include all statuses and descendants. Classifications are editorial or inferred from community fields, not an AMS assessment of the problem.

Subcategories

47A05General (adjoints, conjugates, products, inverses, domains, ranges, etc.)0 47A06Linear relations (multivalued linear operators)0 47A07Forms (bilinear, sesquilinear, multilinear)0 47A08Operator matrices0 47A10Spectrum, resolvent0 47A11Local spectral properties of linear operators0 47A12Numerical range, numerical radius2 47A13Several-variable operator theory (spectral, Fredholm, etc.)0 47A15Invariant subspaces of linear operators0 47A16Cyclic vectors, hypercyclic and chaotic operators0 47A20Dilations, extensions, compressions of linear operators0 47A25Spectral sets of linear operators0 47A30Norms (inequalities, more than one norm, etc.) of linear operators0 47A35Ergodic theory of linear operators0 47A40Scattering theory of linear operators0 47A45Canonical models for contractions and nonselfadjoint linear operators0 47A46Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.0 47A48Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc.0 47A50Equations and inequalities involving linear operators, with vector unknowns0 47A52Linear operators and ill-posed problems, regularization0 47A53(Semi-) Fredholm operators; index theories0 47A55Perturbation theory of linear operators0 47A56Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)0 47A57Linear operator methods in interpolation, moment and extension problems0 47A58Linear operator approximation theory0 47A60Functional calculus for linear operators0 47A62Equations involving linear operators, with operator unknowns0 47A63Linear operator inequalities0 47A64Operator means involving linear operators, shorted linear operators, etc.0 47A65Structure theory of linear operators0 47A66Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal linear operators0 47A67Representation theory of linear operators0 47A68Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators0 47A70(Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces0 47A75Eigenvalue problems for linear operators0 47A80Tensor products of linear operators0 47A99General theory of linear operators0

Mapped problems

OP-12127AnalysisStatus unassessed

Crouzeix's Conjecture (AlphaEvolve problem 25)

Crouzeix's Conjecture (AlphaEvolve problem 25). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.

AlphaEvolve Repository of Problems — Georgiev, Gómez-Serrano, Tao & Wagner· Licensed source statement· 2025

OP-11993AnalysisSolved

Crouzeix constant ( $C_{2}$ )

Crouzeix constant: determine C 2 or improve its bounds; the repository records 2 (lower) and 2 (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

Journals & articles in MSC 47

These are selected sources for the parent class. Article coverage is a first reviewed selection, and may not cover this exact subcategory.

Analysis & PDE ↗

Mathematical Sciences Publishers

Analysis and partial differential equations

Journal discovery is available; article-level extraction for this class is not yet included in this batch.

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MSC2020 © Mathematical Reviews (AMS) and zbMATH · CC BY-NC-SA 4.0 · Official PDF, page 125