Operator theory Basic notions: bounded and unbounded operators Concept
Operator norm
Summary
The operator norm of a continuous linear map measures the largest factor by which the map can stretch a vector. It makes the space of continuous linear maps into a normed space.
Where this leads
63 pages build on this one.
- von Neumann stability analysis
- Convergence of the Neumann series for Volterra kernels
- Toeplitz algebra
- Exponential of a bounded operator
- Stein interpolation theorem
- Calkin algebra
- Pseudospectrum
- Landweber iteration
- Neumann series
- Alternating-direction implicit method
- Nash–Moser theorem
- Ideal of compact operators
- Atkinson's theorem
- Riesz–Thorin theorem
- Bauer–Fike theorem
- Analytic function between Banach spaces
- Algebra of bounded operators on a Hilbert space
- Von Neumann bicommutant theorem
- Implicit function theorem in Banach spaces
- Ultraweak topology
- Entropic uncertainty principle
- Lax equivalence theorem
- Hilbert space adjoint
- Differential equations in Banach spaces
- Weak operator topology
- Born series
- Von Neumann algebra
- Babenko–Beckner inequality
- Continuous function with divergent Fourier series
- Reduction of a first-kind Volterra equation to the second kind
- Liouville–Neumann series
- Hausdorff–Young inequality
- Eckart–Young theorem
- Spectral radius formula
- Inverse function theorem in Banach spaces
- Dual operator
- Crank–Nicolson method
- Nest algebra
- Lebesgue constant
- Oseledets theorem
- Dvoretzky's theorem
- Contraction semigroup
- Murray–von Neumann classification of factors
- Condition number
- Iterative refinement
- Weyl's inequality
- Banach–Mazur compactum
- Operator space
- Kaplansky density theorem
- Spectral triple
- Banach–Mazur distance
- Pesin theory
- Nyström method
- Operator Cauchy equation and one-parameter semigroups
- Strong operator topology
- Unique solvability of Volterra equations of the second kind
- Lebesgue's lemma on near-best approximation
- Cotlar–Stein lemma
- Numerical range
- Uniform boundedness principle
- Reflexive operator algebra
- Commutant
- C0-semigroup
Further reading
- Web https://en.wikipedia.org/wiki/Operator_norm, lead section
About this page
| Tag | 06EKW1AKXF |
|---|---|
| URI | m2://06EKW1AKXF |
| Aliases | norm-of-a-linear-map |
| Kind | concept |
| Writing | W1 stated |
| MSC | 47A30 |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
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What links here
Definitions
Used by
- Exponential of a bounded operator
- Pseudospectrum
- Landweber iteration
- Neumann series
- Riesz–Thorin theorem
- Bauer–Fike theorem
- Analytic function between Banach spaces
- Algebra of bounded operators on a Hilbert space
- Lax equivalence theorem
- Hilbert space adjoint
- Differential equations in Banach spaces
- Born series
- Eckart–Young theorem
- Spectral radius formula
- Inverse function theorem in Banach spaces
- Dual operator
- Lebesgue constant
- Oseledets theorem
- Contraction semigroup
- Condition number
- Iterative refinement
- Weyl's inequality
- Banach–Mazur compactum
- Operator space
- Banach–Mazur distance
- Operator Cauchy equation and one-parameter semigroups
- Lebesgue's lemma on near-best approximation
- Cotlar–Stein lemma
- Numerical range
- Uniform boundedness principle
- C0-semigroup