Operator theory Basic notions: bounded and unbounded operators Concept
Continuous linear map
Summary
A continuous linear map between normed spaces is a linear map that is continuous for the norm topologies. Such maps are the same as the bounded linear maps, which multiply lengths by at most a fixed constant.
Where this leads
50 pages build on this one.
- Schur test
- Nuclear operator
- Convergence of the Neumann series for Volterra kernels
- Exponential of a bounded operator
- Saturation of approximation methods
- Neumann series
- Tempered distribution
- Nash–Moser theorem
- Atkinson's theorem
- Implicit function theorem in Banach spaces
- Hilbert space adjoint
- Continuous dual space
- Strictly singular operator
- Finite-rank operator
- Continuous function with divergent Fourier series
- Fredholm map
- Reduction of a first-kind Volterra equation to the second kind
- Closed graph theorem
- Liouville–Neumann series
- Schauder's theorem on adjoints of compact operators
- Approximation property
- Trace operator
- Spectral radius formula
- Inverse function theorem in Banach spaces
- Dual operator
- Unbounded operator
- Hankel operator
- Bounded inverse theorem
- Influence function
- Hilbert–Schmidt operator
- Gaussian measure
- Closed operator
- Nilpotent operator
- Choquet theory
- Gateaux derivative
- Reproducing kernel Hilbert space
- Fredholm operator
- Operator theory
- Resolvent
- Integral transforms of tempered distributions
- Interpolation space
- Nyström method
- Unique solvability of Volterra equations of the second kind
- Spectrum of an operator
- Invertible operator
- Numerical range
- Uniform boundedness principle
- Abstract Wiener space
- Tikhonov regularization
- Hellinger–Toeplitz theorem
Further reading
- Web https://en.wikipedia.org/wiki/Bounded_operator, lead section
About this page
| Tag | 03TM135G0N |
|---|---|
| URI | m2://03TM135G0N |
| Aliases | bounded-linear-operator, bounded-operator |
| Kind | concept |
| Writing | W1 stated |
| MSC | 47B01 |
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What links here
Definitions
Used by
- Schur test
- Nuclear operator
- Exponential of a bounded operator
- Saturation of approximation methods
- Neumann series
- Tempered distribution
- Atkinson's theorem
- Hilbert space adjoint
- Continuous dual space
- Strictly singular operator
- Finite-rank operator
- Closed graph theorem
- Schauder's theorem on adjoints of compact operators
- Approximation property
- Trace operator
- Spectral radius formula
- Dual operator
- Unbounded operator
- Hankel operator
- Bounded inverse theorem
- Hilbert–Schmidt operator
- Gaussian measure
- Nilpotent operator
- Choquet theory
- Gateaux derivative
- Reproducing kernel Hilbert space
- Fredholm operator
- Operator theory
- Resolvent
- Interpolation space
- Spectrum of an operator
- Invertible operator
- Numerical range
- Uniform boundedness principle
- Abstract Wiener space
- Tikhonov regularization
- Hellinger–Toeplitz theorem