Category:Banach spaces

• Banach space

A

• Approximation property
• Asplund space
• Aubin–Lions lemma
• Auerbach's lemma

B

• B-convex space
• Ba space
• Banach bundle (non-commutative geometry)
• Banach bundle
• Banach manifold
• List of Banach spaces
• Banach-Saks property
• Barron space
• Bergman space
• Besov space
• Bishop–Phelps theorem
• BK-space
• Bounded variation
• Browder–Minty theorem
• Bs space

C

• C space
• Clarkson's inequalities
• Closed range theorem
• Crinkled arc
• Cylindrical σ-algebra

D

• Differentiable vector-valued functions from Euclidean space
• Differentiation in Fréchet spaces
• Dunford–Pettis property
• Dvoretzky's theorem

E

• Eberlein–Šmulian theorem
• Ehrling's lemma

F

• Fichera's existence principle
• Fréchet derivative
• Fredholm kernel
• Fundamental lemma of interpolation theory

G

• Girth (functional analysis)
• Goldstine theorem
• Grothendieck space

H

• Hanner's inequalities

I

• Infinite-dimensional holomorphy
• Infinite-dimensional Lebesgue measure
• Infinite-dimensional vector function
• Interpolation space
• Itô–Nisio theorem

J

• James' space

K

• Krein–Smulian theorem

L

• L-infinity
• Lomonosov's invariant subspace theorem
• Lorentz space
• Lp space
• Lp sum

M

• Maharam's theorem
• Mazur's lemma
• Method of continuity
• Milman–Pettis theorem
• Modulation space
• Modulus and characteristic of convexity
• Morrey–Campanato space
• Multipliers and centralizers (Banach spaces)

O

• Operator space
• Opial property
• Orlicz space

P

• Polynomially reflexive space
• Pseudo-monotone operator

Q

• Quasi-derivative
• Quotient of subspace theorem

R

• Radonifying operator
• Reflexive space
• Riesz–Thorin theorem

S

• Schauder basis
• Semi-reflexive space
• Souček space
• Space of continuous functions on a compact space
• Strong operator topology
• Strongly measurable function
• Structure theorem for Gaussian measures

T

• Tsirelson space
• Type and cotype of a Banach space

U

• Uniform norm
• Uniformly convex space
• Uniformly smooth space

Y

• Young function