Uniform algebras

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Information for Authority record

Name (Hebrew)
אלגברות אחידות
Name (Latin)
Uniform algebras
Name (Arabic)
الجبر الموحدة
Other forms of name
Algebras, Uniform
See Also From tracing topical name
Banach algebras
Commutative algebra
Function algebras
MARC
MARC

Other Identifiers

Wikidata: Q7885096
Library of congress: sh 85139687

Wikipedia description:

In functional analysis, a uniform algebra A on a compact Hausdorff space X is a closed (with respect to the uniform norm) subalgebra of the C*-algebra C(X) (the continuous complex-valued functions on X) with the following properties: the constant functions are contained in A for every x , y ∈ X {\displaystyle x,y\in X} there is f ∈ A {\displaystyle f\in A} with f ( x ) ≠ f ( y ) {\displaystyle f(x)\neq f(y)} . This is called separating the points of X. As a closed subalgebra of the commutative algebra (structure) Banach algebra C(X), a uniform algebra is itself a unital commutative Banach algebra (when equipped with the uniform norm). Hence, it is (by definition) a Banach function algebra. A uniform algebra A on X is said to be natural if the maximal ideals of A are precisely the ideals M x {\displaystyle M_{x}} of functions vanishing at a point x in X.

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