Functional analysis Normed and Banach spaces Concept
Normed vector space
Summary
A normed vector space is a real or complex vector space together with a norm.
Where this leads
59 pages build on this one.
- Reflexive space
- Namioka--Phelps
- Ill-posedness of real Laplace inversion
- n-term approximation
- Neural network approximation
- Jordan–von Neumann theorem
- Mazur–Ulam theorem
- Ryll-Nardzewski fixed-point theorem
- Multivariate approximation
- Schaefer's fixed point theorem
- Normed algebra
- Mazur's lemma
- Aoki–Rassias theorem
- Compact operator
- Existence of best approximations from finite-dimensional subspaces
- Quotient of a normed space
- Leray–Schauder method
- Fenchel conjugate
- Error of best approximation
- Space of functions of bounded variation
- Iterative method
- Space of bounded continuous functions
- Nonlinear approximation
- Schauder fixed-point theorem
- Bidual and canonical embedding
- Finite-rank operator
- Continuous function with divergent Fourier series
- Well-posed problem
- Inverse problem
- Lomonosov's invariant subspace theorem
- Schauder fixed-point theorem for integral equations
- Goldstine theorem
- Ill-posedness of first-kind equations
- Dual operator
- Unbounded operator
- Function approximation
- Chebyshev set
- Influence function
- Approximation theory
- Completion of a normed space
- Dvoretzky's theorem
- Fenchel–Young inequality
- Gateaux derivative
- Uniformly convex space
- Operator theory
- Banach–Mazur compactum
- Mosco convergence
- Strictly convex space
- Banach algebra
- Approximately additive function
- Banach–Mazur distance
- Hyers' theorem
- Nyström method
- Lebesgue's lemma on near-best approximation
- Information-based complexity
- Best approximation
- Fenchel–Moreau theorem
- Invertible operator
- Uniform boundedness principle
Further reading
About this page
| Tag | 03J5RAKB30 |
|---|---|
| URI | m2://03J5RAKB30 |
| Kind | concept |
| Writing | W1 stated |
| MSC | 46B20 |
| Same as |
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What links here
Definitions
Special cases
Used by
- Reflexive space
- n-term approximation
- Neural network approximation
- Jordan–von Neumann theorem
- Mazur–Ulam theorem
- Ryll-Nardzewski fixed-point theorem
- Multivariate approximation
- Normed algebra
- Mazur's lemma
- Aoki–Rassias theorem
- Compact operator
- Existence of best approximations from finite-dimensional subspaces
- Quotient of a normed space
- Fenchel conjugate
- Error of best approximation
- Space of functions of bounded variation
- Iterative method
- Space of bounded continuous functions
- Nonlinear approximation
- Schauder fixed-point theorem
- Bidual and canonical embedding
- Finite-rank operator
- Well-posed problem
- Inverse problem
- Goldstine theorem
- Ill-posedness of first-kind equations
- Dual operator
- Unbounded operator
- Function approximation
- Chebyshev set
- Approximation theory
- Completion of a normed space
- Dvoretzky's theorem
- Fenchel–Young inequality
- Gateaux derivative
- Uniformly convex space
- Operator theory
- Banach–Mazur compactum
- Mosco convergence
- Strictly convex space
- Approximately additive function
- Banach–Mazur distance
- Hyers' theorem
- Lebesgue's lemma on near-best approximation
- Information-based complexity
- Best approximation
- Fenchel–Moreau theorem
- Invertible operator
- Uniform boundedness principle