mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A {\displaystyle A} over the real or complex...

functional analysis, a Banach space (/ˈbɑː.nʌx/, Polish pronunciation: [ˈba.nax]) is a complete normed vector space. Thus, a Banach space is a vector space...

mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties...

of representing commutative Banach algebras as algebras of continuous functions; the fact that for commutative C*-algebras, this representation is an isometric...

functional analysis, a Banach function algebra on a compact Hausdorff space X is unital subalgebra, A, of the commutative C*-algebra C(X) of all continuous...

In mathematics, Banach algebra cohomology of a Banach algebra with coefficients in a bimodule is a cohomology theory defined in a similar way to Hochschild...

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

a Banach algebra or ring (generally without an identity) that acts as a substitute for an identity element. A right approximate identity in a Banach algebra...

specifically in functional analysis, a Banach algebra, A, is amenable if all bounded derivations from A into dual Banach A-bimodules are inner (that is of...

\|g\|.\,} Thus the Wiener algebra is a commutative unitary Banach algebra. Also, A(T) is isomorphic to the Banach algebra l1(Z), with the isomorphism...

operator algebras are real or complex Jordan algebras with the compatible structure of a Banach space. When the coefficients are real numbers, the algebras are...

The space of bounded linear operators B(X) on a Banach space X is an example of a unital Banach algebra. Since the definition of the spectrum does not...

the group algebra is any of various constructions to assign to a locally compact group an operator algebra (or more generally a Banach algebra), such that...

∈ A . {\displaystyle x,y\in A.} A complete quasinormed algebra is called a quasi-Banach algebra. A topological vector space (TVS) is a quasinormed space...

be true in general. This conjecture states that every algebra homomorphism from the Banach algebra C(X) (continuous complex-valued functions on X, where...

The Banach–Tarski paradox is a theorem in set-theoretic geometry that states the following: Given a solid ball in three-dimensional space, there exists...

operator algebra is usually used in reference to algebras of bounded operators on a Banach space or, even more specifically in reference to algebras of operators...

composition *-algebra, An algebra with a notion of adjoints C*-algebra, a Banach algebra equipped with a unary involution operation Von Neumann algebra (or W*-algebra)...

operators A : X → X form an associative algebra (using composition of operators as multiplication); this is a Banach algebra. Given any topological space X, the...

isomorphic to the complex numbers, i. e., the only complex Banach algebra that is a division algebra is the complex numbers C {\displaystyle \mathbb {C} }...

by construction, it becomes a uniform algebra and a commutative Banach algebra. By construction, the disc algebra is a closed subalgebra of the Hardy space...

abstractly as C*-algebras that have a predual; in other words the von Neumann algebra, considered as a Banach space, is the dual of some other Banach space called...

article. Banach, a Polish-language surname 16856 Banach, a minor planet Banach algebra, an associative algebra Banach space, a complete normed vector space...

is called the matrix exponential) and more generally in any unital Banach algebra B. In this setting, e0 = 1, and ex is invertible with inverse e−x for...

Normed division algebra Stone–Weierstrass theorem Banach algebra *-algebra B*-algebra C*-algebra Universal C*-algebra Spectrum of a C*-algebra Positive element...

closed subalgebra of the commutative Banach algebra C(X) a uniform algebra is itself a unital commutative Banach algebra (when equipped with the uniform norm)...

mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure...

involutive Banach algebras is an algebra homomorphism preserving *. abelian Synonymous with "commutative"; e.g., an abelian Banach algebra means a commutative...

supremum norm ‖f‖ = supa ≤ x ≤ b |f (x)| is a Banach algebra, (that is, an associative algebra and a Banach space such that ‖fg‖ ≤ ‖f‖·‖g‖ for all  f, g)...

reasonable topology. See for example normed division algebras and Banach algebras. If the division algebra is not assumed to be associative, usually some weaker...