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...

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...

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...

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...

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

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...

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...

∈ 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...

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

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...

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...

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} }...

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...

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)...

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

\|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...

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 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...

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

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

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...

is a homomorphism of Banach algebras from L 1 {\displaystyle L^{1}} equipped with the convolution operation to the Banach algebra of continuous functions...

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...

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)...

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...

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...

variables on Banach spaces. For a product space, the cylinder σ-algebra is the one that is generated by cylinder sets. In the context of a Banach space X {\displaystyle...

ring). *-algebra Affine Lie algebra Akivis algebra Algebra for a monad Albert algebra Alternative algebra AW*-algebra Azumaya algebra Banach algebra Birman–Wenzl...