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
23 pages build on this one.
- Rigged Hilbert space
- Banach–Alaoglu theorem
- Weak topology
- Nuclear operator
- Hahn–Banach separation theorem
- Character space
- Hilbert space adjoint
- Amenable Banach algebra
- Bidual and canonical embedding
- James's theorem
- Schauder's theorem on adjoints of compact operators
- Strong dual space
- Palais–Smale compactness condition
- Dual operator
- Duality of Lp spaces
- Browder–Minty theorem
- Krein–Smulian theorem
- State on a C*-algebra
- Bishop–Phelps theorem
- Mackey–Arens theorem
- Injective tensor product
- Riesz representation theorem
- Dunford–Pettis property
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 |
| Changed | 2 November 2026 |
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What links here
Used by
- Rigged Hilbert space
- Banach–Alaoglu theorem
- Weak topology
- Nuclear operator
- Hahn–Banach separation theorem
- Character space
- Amenable Banach algebra
- Bidual and canonical embedding
- James's theorem
- Schauder's theorem on adjoints of compact operators
- Strong dual space
- Palais–Smale compactness condition
- Dual operator
- Duality of Lp spaces
- Browder–Minty theorem
- Krein–Smulian theorem
- State on a C*-algebra
- Bishop–Phelps theorem
- Mackey–Arens theorem
- Injective tensor product
- Riesz representation theorem
- Dunford–Pettis property
Results about this
- Banach–Alaoglu theorem
- Hahn–Banach separation theorem
- Bishop–Phelps theorem
- Riesz representation theorem