Banach–Stone theorem is a classical result in the theory of continuous functions on topological spaces, named after the mathematicians Stefan Banach and...

that bear Banach's name include Banach spaces, Banach algebras, Banach measures, the Banach–Tarski paradox, the Hahn–Banach theorem, the Banach–Steinhaus...

with the w*-topology, is homeomorphic to K . {\displaystyle K.} Banach–Stone Theorem—If K {\displaystyle K} and L {\displaystyle L} are compact Hausdorff...

Marshall H. Stone considerably generalized the theorem and simplified the proof. His result is known as the Stone–Weierstrass theorem. The Stone–Weierstrass...

Atkinson's theorem (operator theory) Babuška–Lax–Milgram theorem (partial differential equations) Banach–Stone theorem (operator theory) Bauer–Fike theorem (spectral...

theory. The theorem has been the starting point for what is now called Stone duality. In 1937, he published the Stone–Weierstrass theorem which generalized...

in the study of Banach spaces. They are used, for example, in generalizations of the Banach–Stone theorem. Let (X, ‖·‖) be a Banach space over a field...

the Hille–Yosida theorem characterizes the generators of strongly continuous one-parameter semigroups of linear operators on Banach spaces. It is sometimes...

Stefan Banach (explicitly in dimension 3, without stating the theorem in the n-dimensional case), and also years later called the Stone–Tukey theorem after...

Banach algebras. The binomial theorem also holds for two commuting elements of a Banach algebra. The set of invertible elements in any unital Banach algebra...

Hausdorff space is a commutative C*-algebra, and conversely by the Banach–Stone theorem one can recover the topology of the space from the algebraic properties...

Banach-Schauder theorem Banach–Steinhaus theorem Banach–Stone theorem Banach–Tarski paradox Banach's matchbox problem Hahn–Banach theorem 16856 Banach Banach Journal...

Tychonoff's theorem has been used to prove many other mathematical theorems. These include theorems about compactness of certain spaces such as the Banach–Alaoglu...

(signed) Borel measures on the Stone–Čech compactification of the natural numbers. "Banach limit". PlanetMath. Conway, Theorem III.7.1 Balcar-Štěpánek, 8...

algebra of scalars, indeed functorially so; this is the content of the Banach–Stone theorem. Indeed, any commutative C*-algebra can be realized as the algebra...

In mathematics, Stone's theorem on one-parameter unitary groups is a basic theorem of functional analysis that establishes a one-to-one correspondence...

category theorem Open mapping theorem (functional analysis) Closed graph theorem Uniform boundedness principle Arzelà–Ascoli theorem Banach–Alaoglu theorem Measure...

but also as a topological space – this is an application of the Banach–Stone theorem, and is more formally known as the spectrum of a C*-algebra. First...

proved Tychonoff's theorem). In 1937, Čech extended Tychonoff's technique and introduced the notation βX for this compactification. Stone also constructed...

out to be locally compact and Hausdorff. (This follows from the Banach–Alaoglu theorem.) The space Φ A {\displaystyle \Phi _{A}} is compact (in the topology...

type of Lipschitz continuity, called contraction, is used in the Banach fixed-point theorem. We have the following chain of strict inclusions for functions...

Stone duality, Stone's theorem on one-parameter unitary groups, Banach–Stone theorem Antonio Stradivari, Italian violin builder – Stradivari. Gregor Strasser...

general Banach spaces. The open mapping theorem is equivalent to the closed graph theorem, which asserts that a linear function from one Banach space to...

commutative algebras, Banach–Stone theorem Local rings: Gorenstein local ring (also used in Wiles's proof of Fermat's Last Theorem): Duality (mathematics)...

can be used to prove the Hahn-Banach theorem and the Alexander subbase theorem. Intuitively, the Boolean prime ideal theorem states that there are "enough"...

Functional analysis The Hahn–Banach theorem in functional analysis, allowing the extension of linear functionals. The theorem that every Hilbert space has...

functions A = C ∞ ( M ) , {\displaystyle A=C^{\infty }(M),} as in the Banach–Stone theorem. Vector bundles over M {\displaystyle M} correspond to projective...

\mathbb {R} } or C , {\displaystyle \mathbb {C} ,} then the Hahn–Banach separation theorem implies that continuous linear functionals on X {\displaystyle...

theorems Complete space Cauchy sequence Banach fixed-point theorem Polish space Hausdorff distance Intrinsic metric Category of metric spaces Stone duality...

convex local base for the zero vector is strong enough for the Hahn–Banach theorem to hold, yielding a sufficiently rich theory of continuous linear functionals...