Functional analysis Duality for topological vector spaces Concept
Continuous dual space
Summary
The continuous dual space of a topological vector space is the vector space of all continuous linear forms on . It is a subspace of the algebraic dual space, usually much smaller in infinite dimension. For a normed space it is a Banach space with the dual norm. Duality theory studies through and the topologies on both, such as the weak topology and the strong dual topology.
Where this leads
41 pages build on this one.
- Rigged Hilbert space
- Banach–Alaoglu theorem
- Weak topology
- Namioka--Phelps
- Nuclear operator
- Céa's lemma
- Hahn–Banach separation theorem
- Lax–Milgram theorem
- Minimum total potential energy principle
- Character space
- Hilbert space adjoint
- Supporting hyperplane theorem
- Amenable Banach algebra
- Straszewicz's theorem
- Bidual and canonical embedding
- James's theorem
- Lions–Stampacchia theorem
- Schauder's theorem on adjoints of compact operators
- Strong dual space
- Palais–Smale compactness condition
- Dual operator
- Duality of Lp spaces
- Galerkin method
- Fefferman duality theorem
- Clarke generalized gradient
- Monotone operator method for Hammerstein equations
- Fenchel–Young inequality
- Minkowski–Carathéodory theorem
- Browder–Minty theorem
- Krein–Smulian theorem
- State on a C*-algebra
- Bishop–Phelps theorem
- Signorini problem
- Mackey–Arens theorem
- Mosco convergence
- Petrov–Galerkin method
- Injective tensor product
- Ladyzhenskaya–Babuška–Brezzi condition
- Riesz representation theorem
- Dunford–Pettis property
- Fenchel–Moreau theorem
Further reading
- Web https://en.wikipedia.org/wiki/Dual_space, Continuous dual space
About this page
| Tag | 4A82S5FVRT |
|---|---|
| URI | m2://4A82S5FVRT |
| Kind | concept |
| Writing | W0 stub |
| MSC | 46A20 |
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What links here
Used by
- Rigged Hilbert space
- Banach–Alaoglu theorem
- Weak topology
- Namioka--Phelps
- Nuclear operator
- Céa's lemma
- Hahn–Banach separation theorem
- Lax–Milgram theorem
- Character space
- Amenable Banach algebra
- Bidual and canonical embedding
- James's theorem
- Lions–Stampacchia theorem
- Schauder's theorem on adjoints of compact operators
- Strong dual space
- Palais–Smale compactness condition
- Dual operator
- Duality of Lp spaces
- Galerkin method
- Fefferman duality theorem
- Clarke generalized gradient
- Fenchel–Young inequality
- Browder–Minty theorem
- Krein–Smulian theorem
- State on a C*-algebra
- Bishop–Phelps theorem
- Mackey–Arens theorem
- Mosco convergence
- Petrov–Galerkin method
- Injective tensor product
- Ladyzhenskaya–Babuška–Brezzi condition
- Riesz representation theorem
- Dunford–Pettis property
- Fenchel–Moreau theorem
Results about this
- Banach–Alaoglu theorem
- Hahn–Banach separation theorem
- Bishop–Phelps theorem
- Riesz representation theorem