Category
page 1Theorems in functional analysis
Hölder's inequality
inequality between integrals in Lp spaces
Hahn–Banach theorem
theorem on extension of bounded linear functionals
Bessel's inequality
theorem
uniform boundedness principle
theorem that a pointwise bounded set of linear operators on a Banach space is uniformly bounded in operator norm
Parseval's identity
mathematical concept
open mapping theorem
Theorem that surjective continuous operators on Banach spaces are open maps
Riesz representation theorem
theorem
closed graph theorem
theorem
Banach–Alaoglu theorem
theorem
spectral theorem
theorem
Arzelà–Ascoli theorem
theorem
Plancherel theorem
theorem in harmonic analysis
Krein–Milman theorem
theorem
Lions–Lax–Milgram theorem
a result in functional analysis with applications in the study of partial differential equations
Schauder fixed point theorem
theorem that a continuous mapping of a convex subset of a topological vector space into a compact subset of itself has a fixed point
Gelfand–Mazur theorem
Kirszbraun theorem
mathematical theorem related to real and functional analysis
Hellinger–Toeplitz theorem
theorem
Gelfand–Naimark theorem
mathematics theorem in functional analysis
Dvoretzky's theorem
Mazur–Ulam theorem
theorem
Riesz–Markov–Kakutani representation theorem
statement about linear functionals and measures
Ryll-Nardzewski fixed-point theorem
theorem
Markov–Kakutani fixed-point theorem
Banach–Mazur theorem
Eberlein–Šmulian theorem
Relates three different kinds of weak compactness in a Banach space
Fredholm's theorem
Dieudonné's theorem
Nash–Moser theorem
Generalization of the inverse function theorem
Riesz–Thorin theorem
theorem
weak formulation
theorem
Banach–Stone theorem
Min-max theorem
variational characterization of eigenvalues of compact Hermitian operators on Hilbert spaces
Hilbert projection theorem
on closed convex subsets in Hilbert space
James' theorem
theorem in mathematics
Bochner's theorem
theorem of Fourier transforms of Borel measures
Hille–Yosida theorem
theorem
Mazur's lemma
On strongly convergent combinations of weakly convergent sequence in a Banach space