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List of functional analysis topics
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<h2 id="hilbert-space">Hilbert space</h2> <ul><li><a href="/facts/Bra%E2%80%93ket_notation/NDlKsaRh">Bra–ket notation</a></li> <li><a href="/facts/Definite_bilinear_form/utlBuVpN">Definite bilinear form</a></li> <li><a href="/facts/Direct_integral/UerMgqEb">Direct integral</a></li> <li><a href="/facts/Euclidean_space/R2UbzmzM">Euclidean space</a></li> <li><a href="/facts/Fundamental_theorem_of_Hilbert_spaces/o41hQyjm">Fundamental theorem of Hilbert spaces</a></li> <li><a href="/facts/Gram%E2%80%93Schmidt_process/vRNpld3t">Gram–Schmidt process</a></li> <li><a href="/facts/Hellinger%E2%80%93Toeplitz_theorem/1S36FmQg">Hellinger–Toeplitz theorem</a></li> <li><a href="/facts/Hilbert_space/aDFMh4lV">Hilbert space</a></li> <li><a href="/facts/Inner_product_space/HoyjElEy">Inner product space</a></li> <li><a href="/facts/Legendre_polynomials/nDvV4em0">Legendre polynomials</a></li> <li><a href="/facts/Matrix_(mathematics)/qa8FI4ko">Matrices</a></li> <li><a href="/facts/Mercer%27s_theorem/6CmBHnHc">Mercer's theorem</a></li> <li><a href="/facts/Min-max_theorem/2KJHjoAw">Min-max theorem</a></li> <li><a href="/facts/Normal_vector/jhtLIhcu">Normal vector</a></li> <li><a href="/facts/Orthonormal_basis/pzfKHlJG">Orthonormal basis</a></li> <li><a href="/facts/Orthogonal_complement/a13oQBsz">Orthogonal complement</a></li> <li><a href="/facts/Orthogonalization/7rwygMJt">Orthogonalization</a></li> <li><a href="/facts/Parallelogram_law/JI1LwPxd">Parallelogram law</a> <ul><li><a href="/facts/Normal_matrix/WVKxrEK9">Normal matrix</a>, <a href="/facts/Normal_operator/lwtz7tuF">normal operator</a></li> <li><a href="/facts/Orthogonal_matrix/WDXBXYB5">Orthogonal matrix</a></li> <li><a href="/facts/Unitary_matrix/8fsxv3KD">Unitary matrix</a></li></ul></li> <li><a href="/facts/Semi-Hilbert_space/0ECwvDjT">Semi-Hilbert space</a> <ul><li><a href="/facts/Diagonal_matrix/tjIAHrE6">Diagonal matrix</a></li> <li><a href="/facts/Eigenvector/8TjEoT8u">Eigenvector</a>, <a href="/facts/Eigenvalue/8TjEoT8u">eigenvalue</a>, <a href="/facts/Eigenfunction/62EJS0XB">eigenfunction</a></li> <li><a href="/facts/Hermitian_operator/VrH1nEAK">Hermitian operator</a> <a href="/facts/Self-adjoint_operator/VrH1nEAK">self-adjoint operator</a>, <a href="/facts/Hermitian_adjoint/gN6RHphd">Hermitian adjoint</a></li> <li><a href="/facts/Hilbert_matrix/60xPxyzt">Hilbert matrix</a></li> <li><a href="/facts/Shift_operator/6c6lc0ks">Shift operator</a></li> <li><a href="/facts/Symmetric_matrix/08CGwjNl">Symmetric matrix</a></li></ul></li> <li><a href="/facts/Parseval%27s_identity/EukqvgUp">Parseval's identity</a></li> <li><a href="/facts/Rayleigh_quotient/yH7sD1K4">Rayleigh quotient</a></li> <li><a href="/facts/Reproducing_kernel_Hilbert_space/VegkYAXb">Reproducing kernel Hilbert space</a></li> <li><a href="/facts/Riesz_representation_theorem/9CjKDUII">Riesz representation theorem</a></li> <li><a href="/facts/Rigged_Hilbert_space/zQ4UTMMB">Rigged Hilbert space</a></li> <li><a href="/facts/Spectral_theorem/Vqc04B21">Spectral theorem</a>, <a href="/facts/Spectral_theory/8sAEEIMM">Spectral theory</a></li> <li><a href="/facts/Trace_class/2AmWENA3">Trace class</a></li></ul> <h2 id="functional-analysis-classic-results">Functional analysis, classic results</h2> <ul><li><a href="/facts/Normed_vector_space/rmDljfyE">Normed vector space</a></li> <li><a href="/facts/Unit_ball/5UeoTcug">Unit ball</a></li> <li><a href="/facts/Banach_space/sDEIk7EC">Banach space</a></li> <li><a href="/facts/Hahn%E2%80%93Banach_theorem/3AUHusvn">Hahn–Banach theorem</a></li> <li><a href="/facts/Dual_space/4Uw4Knz1">Dual space</a></li> <li><a href="/facts/Predual/jN6kYA24">Predual</a></li> <li><a href="/facts/Weak_topology/XJASE9Up">Weak topology</a></li> <li><a href="/facts/Reflexive_space/g7Cjbw0S">Reflexive space</a></li> <li><a href="/facts/Polynomially_reflexive_space/BTN8LUP0">Polynomially reflexive space</a></li> <li><a href="/facts/Baire_category_theorem/AwodvqgV">Baire category theorem</a></li> <li><a href="/facts/Open_mapping_theorem_(functional_analysis)/nFChD5j5">Open mapping theorem (functional analysis)</a></li> <li><a href="/facts/Closed_graph_theorem/CK2ra00W">Closed graph theorem</a></li> <li><a href="/facts/Uniform_boundedness_principle/rbbdebsr">Uniform boundedness principle</a></li> <li><a href="/facts/Arzel%C3%A0%E2%80%93Ascoli_theorem/eqSFHXbo">Arzelà–Ascoli theorem</a></li> <li><a href="/facts/Banach%E2%80%93Alaoglu_theorem/NILk5nDm">Banach–Alaoglu theorem</a></li> <li><a href="/facts/Measure_of_non-compactness/N2YnzwhB">Measure of non-compactness</a></li> <li><a href="/facts/Banach%E2%80%93Mazur_theorem/vMyrso7L">Banach–Mazur theorem</a></li></ul> <h2 id="operator-theory"><a href="/facts/Operator_theory/Ays1ofel">Operator theory</a></h2> <ul><li><a href="/facts/Bounded_linear_operator/LYmDTIqR">Bounded linear operator</a> <ul><li><a href="/facts/Continuous_linear_extension/efuPh2Gh">Continuous linear extension</a></li> <li><a href="/facts/Compact_operator/KNkcK4mE">Compact operator</a></li> <li><a href="/facts/Approximation_property/Wpft8W1J">Approximation property</a></li> <li><a href="/facts/Invariant_subspace/51Vm1W2X">Invariant subspace</a></li></ul></li> <li><a href="/facts/Spectral_theory/8sAEEIMM">Spectral theory</a> <ul><li><a href="/facts/Spectrum_of_an_operator/cA1evTo6">Spectrum of an operator</a></li> <li><a href="/facts/Essential_spectrum/EHN47PNM">Essential spectrum</a></li> <li><a href="/facts/Spectral_density/q3Rfs7b0">Spectral density</a></li></ul></li> <li><a href="/facts/Topologies_on_the_set_of_operators_on_a_Hilbert_space/bcQKE3DM">Topologies on the set of operators on a Hilbert space</a> <ul><li><a href="/facts/Norm_topology/a5l0TkFW">norm topology</a></li> <li><a href="/facts/Ultrastrong_topology/rMP53oXX">ultrastrong topology</a></li> <li><a href="/facts/Strong_operator_topology/awhSW5op">strong operator topology</a></li> <li><a href="/facts/Weak_operator_topology/upQgUu90">weak operator topology</a></li> <li><a href="/facts/Weak-star_operator_topology/ySc1UXjd">weak-star operator topology</a></li> <li><a href="/facts/Ultraweak_topology/ySc1UXjd">ultraweak topology</a></li></ul></li> <li><a href="/facts/Singular_value/0QWHnqGG">Singular value</a> (or S-number)</li> <li><a href="/facts/Fredholm_operator/FEa1xvxn">Fredholm operator</a></li> <li><a href="/facts/Fuglede%27s_theorem/UCB6QP4J">Fuglede's theorem</a></li> <li><a href="/facts/Compression_(functional_analysis)/6SuygJ9p">Compression (functional analysis)</a></li> <li><a href="/facts/Friedrichs_extension/6JLf1Fcz">Friedrichs extension</a></li> <li><a href="/facts/Stone%27s_theorem_on_one-parameter_unitary_groups/1quJvzU7">Stone's theorem on one-parameter unitary groups</a></li> <li><a href="/facts/Stone%E2%80%93von_Neumann_theorem/4C64mKYR">Stone–von Neumann theorem</a></li> <li><a href="/facts/Functional_calculus/Y84ugVzS">Functional calculus</a> <ul><li><a href="/facts/Continuous_functional_calculus/cJ2Nj9Bo">Continuous functional calculus</a></li> <li><a href="/facts/Borel_functional_calculus/ndGbx2xq">Borel functional calculus</a></li></ul></li> <li><a href="/facts/Hilbert%E2%80%93P%C3%B3lya_conjecture/HuNqSd7Q">Hilbert–Pólya conjecture</a></li></ul> <h2 id="banach-space-examples">Banach space examples</h2> <ul><li><a href="/facts/Lp_space/gbad0Rv1">Lp space</a></li> <li><a href="/facts/Hardy_space/aN45dgx7">Hardy space</a></li> <li><a href="/facts/Sobolev_space/34qxWCyr">Sobolev space</a></li> <li><a href="/facts/Tsirelson_space/6oFm8THf">Tsirelson space</a></li> <li><a href="/facts/Ba_space/CUXe79cw">ba space</a></li></ul> <h2 id="real-and-complex-algebras">Real and complex <a href="/facts/Associative_algebra/DRfoF6KV">algebras</a></h2> <ul><li><a href="/facts/Uniform_norm/5yIkjNE3">Uniform norm</a></li> <li><a href="/facts/Matrix_norm/UJvsb9fF">Matrix norm</a></li> <li><a href="/facts/Spectral_radius/j8T2xrLu">Spectral radius</a></li> <li><a href="/facts/Normed_division_algebra/CW1n5sa0">Normed division algebra</a></li> <li><a href="/facts/Stone%E2%80%93Weierstrass_theorem/QB07Nwba">Stone–Weierstrass theorem</a></li> <li><a href="/facts/Banach_algebra/3BTHdpg2">Banach algebra</a></li> <li><a href="/facts/*-algebra/vcE5TWnT">*-algebra</a></li> <li><a href="/facts/B*-algebra/B3tnGHIo">B*-algebra</a></li> <li><a href="/facts/C*-algebra/B3tnGHIo">C*-algebra</a> <ul><li><a href="/facts/Universal_C*-algebra/7WKHf66p">Universal C*-algebra</a></li> <li><a href="/facts/Spectrum_of_a_C*-algebra/0Ixg4qDc">Spectrum of a C*-algebra</a></li></ul></li> <li><a href="/facts/Positive_element/kvTXwFHj">Positive element</a></li> <li><a href="/facts/Positive_linear_functional/gEGtP6AQ">Positive linear functional</a></li> <li><a href="/facts/Operator_algebra/4fycDNQ1">operator algebra</a> <ul><li><a href="/facts/Nest_algebra/2jP8yYBA">nest algebra</a></li> <li><a href="/facts/Reflexive_operator_algebra/XmFQk6JS">reflexive operator algebra</a></li> <li><a href="/facts/Calkin_algebra/cncF0S4t">Calkin algebra</a></li></ul></li> <li><a href="/facts/Gelfand_representation/QV54f7Jm">Gelfand representation</a></li> <li><a href="/facts/Gelfand%E2%80%93Naimark_theorem/6NuEm48I">Gelfand–Naimark theorem</a></li> <li><a href="/facts/Gelfand%E2%80%93Naimark%E2%80%93Segal_construction/jm6BugY5">Gelfand–Naimark–Segal construction</a></li> <li><a href="/facts/Von_Neumann_algebra/8NyWUIRH">Von Neumann algebra</a> <ul><li><a href="/facts/Abelian_von_Neumann_algebra/Mljk27ba">Abelian von Neumann algebra</a></li></ul></li> <li><a href="/facts/Von_Neumann_double_commutant_theorem/eDcR4s7u">von Neumann double commutant theorem</a> <ul><li><a href="/facts/Commutant/AKhrEUGR">Commutant</a>, <a href="/facts/Bicommutant/kNCH5yHy">bicommutant</a></li></ul></li> <li><a href="/facts/Topological_ring/qxQqzhCy">Topological ring</a></li> <li><a href="/facts/Noncommutative_geometry/WSwggL1p">Noncommutative geometry</a></li> <li><a href="/facts/Disk_algebra/9QVWbISL">Disk algebra</a></li> <li><a href="/facts/Colombeau_algebra/bY55eqfY">Colombeau algebra</a></li></ul> <h2 id="topological-vector-spaces"><a href="/facts/Topological_vector_space/XRex1ChN">Topological vector spaces</a></h2> <ul><li><a href="/facts/Barrelled_space/r2H58TN3">Barrelled space</a></li> <li><a href="/facts/Bornological_space/kpl5B2Ez">Bornological space</a></li> <li><a href="/facts/Bourbaki%E2%80%93Alaoglu_theorem/NILk5nDm">Bourbaki–Alaoglu theorem</a></li> <li><a href="/facts/Dual_pair/2Y8KyofV">Dual pair</a></li> <li><a href="/facts/F-space/NBCcYfcU">F-space</a></li> <li><a href="/facts/Fr%C3%A9chet_space/9gXkQu2u">Fréchet space</a></li> <li><a href="/facts/Krein%E2%80%93Milman_theorem/rAbSnGQt">Krein–Milman theorem</a></li> <li><a href="/facts/Locally_convex_topological_vector_space/AGrPrayC">Locally convex topological vector space</a></li> <li><a href="/facts/Mackey_topology/KI5zwcXv">Mackey topology</a></li> <li><a href="/facts/Mackey%E2%80%93Arens_theorem/uzExVVAD">Mackey–Arens theorem</a></li> <li><a href="/facts/Montel_space/HLXqXHzs">Montel space</a></li> <li><a href="/facts/Polar_set/JY45pfbt">Polar set</a></li> <li><a href="/facts/Polar_topology/WutbMK1V">Polar topology</a></li> <li><a href="/facts/Seminorm/vMuescKp">Seminorm</a></li></ul> <h2 id="amenability">Amenability</h2> <ul><li><a href="/facts/Amenable_group/08XrAwvx">Amenable group</a></li> <li><a href="/facts/Von_Neumann_conjecture/eSfc1SIW">Von Neumann conjecture</a></li></ul> <h2 id="wavelets"><a href="/facts/Wavelet/3XcX4uIP">Wavelets</a></h2> <ul><li><a href="/facts/Basis_function/Bt7jqjY2">Basis function</a></li> <li><a href="/facts/Daubechies_wavelet/lhF1zmqB">Daubechies wavelet</a></li> <li><a href="/facts/Haar_wavelet/F2XIo6yq">Haar wavelet</a></li> <li><a href="/facts/Morlet_wavelet/aTEPLUIM">Morlet wavelet</a></li> <li><a href="/facts/Mexican_hat_wavelet/JvEtddE5">Mexican hat wavelet</a></li> <li><a href="/facts/Complex_Mexican_hat_wavelet/N8u8v2o9">Complex Mexican hat wavelet</a></li> <li><a href="/facts/Hermitian_wavelet/m1z7fyqL">Hermitian wavelet</a></li> <li><a href="/facts/Discrete_wavelet_transform/19DVnk4n">Discrete wavelet transform</a></li> <li><a href="/facts/Continuous_wavelet/TSTvewy4">Continuous wavelet</a></li> <li><a href="/facts/Continuous_wavelet_transform/nGUoUAKX">Continuous wavelet transform</a></li></ul> <h2 id="quantum-theory">Quantum theory</h2> <p><i>See also <a href="/facts/List_of_mathematical_topics_in_quantum_theory/PlQXVQs5">list of mathematical topics in quantum theory</a></i> </p> <ul><li><a href="/facts/Mathematical_formulation_of_quantum_mechanics/fRLw4sFU">Mathematical formulation of quantum mechanics</a></li> <li><a href="/facts/Observable/fcBAsBjm">Observable</a></li> <li><a href="/facts/Operator_(physics)/rCJw8UFz">Operator (physics)</a></li> <li><a href="/facts/Quantum_state/7jbxd7Dx">Quantum state</a> <ul><li><a href="/facts/Pure_state/7jbxd7Dx">Pure state</a></li> <li><a href="/facts/Fock_state/GtFWL7uV">Fock state</a>, <a href="/facts/Fock_space/I2PYLlhl">Fock space</a></li> <li><a href="/facts/Density_state/A1XdylJa">Density state</a></li> <li><a href="/facts/Coherent_state/erY7zuXu">Coherent state</a></li></ul></li> <li><a href="/facts/Heisenberg_picture/Y5XwceMA">Heisenberg picture</a></li> <li><a href="/facts/Density_matrix/A1XdylJa">Density matrix</a></li> <li><a href="/facts/Quantum_logic/yhgQIwyP">Quantum logic</a></li> <li><a href="/facts/Quantum_operation/EhCKTxgn">Quantum operation</a></li> <li><a href="/facts/Wightman_axioms/xbPp5tYp">Wightman axioms</a></li></ul> <h2 id="probability"><a href="/facts/Probability/fgYvMhwb">Probability</a></h2> <ul><li><a href="/facts/Free_probability/xV0lMQry">Free probability</a></li> <li><a href="/facts/Bernstein%27s_theorem_on_monotone_functions/RW16PpPy">Bernstein's theorem</a></li></ul> <h2 id="non-linear">Non-linear</h2> <ul><li><a href="/facts/Fixed-point_theorems_in_infinite-dimensional_spaces/4rJmoRml">Fixed-point theorems in infinite-dimensional spaces</a></li></ul> <h2 id="history">History</h2> <ul><li><a href="/facts/Stefan_Banach/b1qHSNg2">Stefan Banach</a> (1892–1945)</li> <li><a href="/facts/Hugo_Steinhaus/jAvzyLhV">Hugo Steinhaus</a> (1887–1972)</li> <li><a href="/facts/John_von_Neumann/aUk6urof">John von Neumann</a> (1903-1957)</li> <li><a href="/facts/Alain_Connes/tjFJ9Iou">Alain Connes</a> (born 1947)</li> <li><a href="http://www.economics.soton.ac.uk/staff/aldrich/Calculus%20and%20Analysis%20Earliest%20Uses.htm">Earliest Known Uses of Some of the Words of Mathematics: Calculus & Analysis</a></li> <li><a href="http://www.economics.soton.ac.uk/staff/aldrich/matrices.htm">Earliest Known Uses of Some of the Words of Mathematics: Matrices and Linear Algebra</a></li></ul>