Functional analysis Normed and Banach spaces Concept
Banach space
Summary
A Banach space is a normed vector space that is complete for the metric of its norm. Banach spaces are the main setting of functional analysis.
Where this leads
134 pages build on this one.
- Vector measure
- Resolvent set
- Leray–Schauder degree
- Collectively compact operator approximation
- Newton–Kantorovich theorem
- Nonexistence of infinite-dimensional Lebesgue measure
- Eberlein–Šmulian theorem
- Space of convergent sequences c
- Newtonian space
- Namioka--Phelps
- von Neumann stability analysis
- Hilbert–Schmidt expansion theorem
- Nuclear operator
- Complemented subspace
- Lyusternik's theorem on tangent spaces
- Convergence of the Neumann series for Volterra kernels
- Michael selection theorem
- Exponential of a bounded operator
- Type and cotype
- Bloch space
- Monotone operator
- Saturation of approximation methods
- Bilinear series of a symmetric kernel
- Isoperimetric problem of the calculus of variations
- Banach bundle
- Riesz space
- Schaefer's fixed point theorem
- Regularity structures
- Bifurcation from a characteristic value
- Weak lower semicontinuity
- Holomorphy on Banach spaces
- Neumann series
- Alternating-direction implicit method
- Catenary problem
- Abstract Volterra equation
- Aoki–Rassias theorem
- Perturbation theory of linear operators
- Nash–Moser theorem
- Spectral theorem for compact self-adjoint operators
- Courant–Fischer characterization of characteristic values
- Atkinson's theorem
- Milman–Pettis theorem
- Leray–Schauder method
- Bartle–Dunford–Schwartz integral
- Analytic function between Banach spaces
- Hölder space
- Implicit function theorem in Banach spaces
- Euler's elastica
- Lyapunov–Schmidt reduction
- Lax equivalence theorem
- Optimal control of partial differential equations
- James space
- Differential equations in Banach spaces
- Projective tensor product
- Strictly singular operator
- Mountain pass theorem
- Born series
- Lidskii's trace formula for integral operators
- Dido's problem
- Coercive functional
- Continuous function with divergent Fourier series
- Fredholm map
- James's theorem
- Banach lattice
- Analytic semigroup
- Reduction of a first-kind Volterra equation to the second kind
- Spectrum of the Laplace–Beltrami operator
- Closed graph theorem
- Liouville–Neumann series
- Convergence of approximations for second-kind equations
- Schauder's theorem on adjoints of compact operators
- Lomonosov's invariant subspace theorem
- Schauder fixed-point theorem for integral equations
- Spectral theory of compact operators
- Separable Banach space
- Perfectoid space
- Banach analytic space
- Palais–Smale compactness condition
- Approximation property
- Kuratowski embedding
- Spectral radius formula
- Peetre K-functional
- Inverse function theorem in Banach spaces
- Crank–Nicolson method
- Aubin–Lions lemma
- Bounded inverse theorem
- Infinitesimal generator of a Markov process
- Clarke generalized gradient
- Monotone operator method for Hammerstein equations
- Completion of a normed space
- Browder–Minty theorem
- Gaussian measure
- Closed operator
- Krein–Smulian theorem
- Hilbert manifold
- Jentzsch's theorem on positive kernels
- Nilpotent operator
- Bishop–Phelps theorem
- Contraction semigroup
- Mercer's theorem
- Fredholm operator
- Lagrange multipliers on Banach spaces
- Operator theory
- Mild solution
- Tsirelson space
- Injective tensor product
- Generator of a semigroup
- Projection method for integral equations
- Resolvent
- Banach–Lie group
- Singular values of a compact operator
- Interpolation space
- Krein–Rutman theorem
- Banach manifold
- Hyers' theorem
- Nyström method
- Operator Cauchy equation and one-parameter semigroups
- Dunford–Pettis property
- Schmidt's singular value decomposition of a kernel
- Unique solvability of Volterra equations of the second kind
- Riesz–Fischer theorem
- Fredholm's theorem
- Spectrum of an operator
- Invertible operator
- Uniform boundedness principle
- Dissipative operator
- Lumer–Phillips theorem
- Abstract Wiener space
- Anderson–Kadec theorem
- C0-semigroup
- Enflo's counterexample to the approximation problem
- Feller process
- A priori estimate
- Hellinger–Toeplitz theorem
Further reading
- Web https://en.wikipedia.org/wiki/Banach_space, lead section
About this page
| Tag | 06GZ956657 |
|---|---|
| URI | m2://06GZ956657 |
| Aliases | complete-normed-space |
| Kind | concept |
| Writing | W1 stated |
| MSC | 46B99 |
| Specializes | Normed vector space |
| Same as |
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What this page needs for W2
- edge not_instance_of in: at least one non-example (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Instances
- Sequence spaces lp
- p-norm on R^n
- Sup norm on bounded continuous functions
- Space of convergent sequences c
- Classical Wiener space
- James space
- Bounded sequences ℓ∞
- Space of convergent sequences
- Tsirelson space
- Space of null sequences
Definitions
Used by
- Vector measure
- Resolvent set
- Leray–Schauder degree
- Collectively compact operator approximation
- Newton–Kantorovich theorem
- Nonexistence of infinite-dimensional Lebesgue measure
- Eberlein–Šmulian theorem
- Space of convergent sequences c
- Newtonian space
- Namioka--Phelps
- Nuclear operator
- Complemented subspace
- Lyusternik's theorem on tangent spaces
- Michael selection theorem
- Exponential of a bounded operator
- Type and cotype
- Bloch space
- Monotone operator
- Saturation of approximation methods
- Schaefer's fixed point theorem
- Regularity structures
- Bifurcation from a characteristic value
- Weak lower semicontinuity
- Holomorphy on Banach spaces
- Neumann series
- Abstract Volterra equation
- Aoki–Rassias theorem
- Perturbation theory of linear operators
- Atkinson's theorem
- Milman–Pettis theorem
- Leray–Schauder method
- Bartle–Dunford–Schwartz integral
- Analytic function between Banach spaces
- Hölder space
- Implicit function theorem in Banach spaces
- Lyapunov–Schmidt reduction
- Lax equivalence theorem
- Optimal control of partial differential equations
- James space
- Differential equations in Banach spaces
- Projective tensor product
- Strictly singular operator
- Mountain pass theorem
- Born series
- Coercive functional
- James's theorem
- Banach lattice
- Analytic semigroup
- Closed graph theorem
- Convergence of approximations for second-kind equations
- Schauder's theorem on adjoints of compact operators
- Lomonosov's invariant subspace theorem
- Spectral theory of compact operators
- Separable Banach space
- Perfectoid space
- Banach analytic space
- Palais–Smale compactness condition
- Approximation property
- Kuratowski embedding
- Spectral radius formula
- Peetre K-functional
- Inverse function theorem in Banach spaces
- Aubin–Lions lemma
- Bounded inverse theorem
- Infinitesimal generator of a Markov process
- Clarke generalized gradient
- Completion of a normed space
- Browder–Minty theorem
- Gaussian measure
- Krein–Smulian theorem
- Nilpotent operator
- Bishop–Phelps theorem
- Contraction semigroup
- Fredholm operator
- Lagrange multipliers on Banach spaces
- Operator theory
- Mild solution
- Tsirelson space
- Injective tensor product
- Generator of a semigroup
- Projection method for integral equations
- Resolvent
- Interpolation space
- Krein–Rutman theorem
- Banach manifold
- Hyers' theorem
- Operator Cauchy equation and one-parameter semigroups
- Dunford–Pettis property
- Riesz–Fischer theorem
- Spectrum of an operator
- Invertible operator
- Uniform boundedness principle
- Dissipative operator
- Lumer–Phillips theorem
- Abstract Wiener space
- Anderson–Kadec theorem
- C0-semigroup
- Enflo's counterexample to the approximation problem
- Feller process
- A priori estimate
Results about this
- Nonexistence of infinite-dimensional Lebesgue measure
- Schaefer's fixed point theorem
- Implicit function theorem in Banach spaces
- Kuratowski embedding
- Inverse function theorem in Banach spaces