The Besov space is one of the Banach spaces. It can be used for solving partial differential equations.
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| Spaces | | | Properties |
- barrelled
- complete
- dual (algebraic/topological)
- locally convex
- reflexive
- separable
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| Theorems |
- Hahn–Banach
- Riesz representation
- closed graph
- uniform boundedness principle
- Kakutani fixed-point
- Krein–Milman
- min–max
- Gelfand–Naimark
- Banach–Alaoglu
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| Operators |
- adjoint
- bounded
- compact
- Hilbert–Schmidt
- normal
- nuclear
- trace class
- transpose
- unbounded
- unitary
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| Algebras |
- Banach algebra
- C*-algebra
- spectrum of a C*-algebra
- operator algebra
- group algebra of a locally compact group
- von Neumann algebra
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| Open problems |
- invariant subspace problem
- Mahler's conjecture
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| Applications |
- Hardy space
- spectral theory of ordinary differential equations
- heat kernel
- index theorem
- calculus of variations
- functional calculus
- integral operator
- Jones polynomial
- topological quantum field theory
- noncommutative geometry
- Riemann hypothesis
- distribution (or generalized functions)
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| Advanced topics |
- approximation property
- balanced set
- Choquet theory
- weak topology
- Banach–Mazur distance
- Tomita–Takesaki theory
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