Category
page 1Banach spaces
Banach space
normed vector space that is complete
Lp space
function spaces generalizing finite-dimensional p norm spaces
Fréchet derivative
a derivative defined on normed spaces
Schauder basis
Computational tool
reflexive space
locally convex topological vector space that coincides with the continuous dual of its continuous dual space, both as linear space and as topological space
uniform norm
p-norm for p equal to ∞

Birnbaum–Orlicz space
topological space
uniformly convex space
reflexive Banach space such that the center of a line segment inside the unit ball must lie deep inside the unit ball unless the segment is short
Dvoretzky's theorem
Besov space
generalization of Sobolev spaces
Lorentz space
function space
Clarkson's inequalities
inequality on Lp norms
Eberlein–Šmulian theorem
Relates three different kinds of weak compactness in a Banach space
James' space
Cylindrical σ-algebra
Riesz–Thorin theorem
theorem
Mazur's lemma
On strongly convergent combinations of weakly convergent sequence in a Banach space