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

specifically in functional analysis, a Banach space (pronounced [ˈbanax]) is a complete normed vector space. Thus, a Banach space is a vector space with a metric...

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...

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

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

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)...

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...

for which the argument is a matrix, or even an element of a Banach algebra or a Lie algebra. The importance of the exponential function in mathematics...

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...

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...

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...

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...

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...

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

\|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...

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...

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)...

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...

an algebra. This property follows directly from the fact that BV ⁡ ( Ω ) {\displaystyle \operatorname {\operatorname {BV} } (\Omega )} is a Banach space...

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...

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

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...

algebra with this property is called a Banach algebra. It is possible to generalize spectral theory to such algebras. C*-algebras, which are Banach algebras...

Banach algebra Amenable Banach algebra Banach Jordan algebra Banach function algebra Banach *-algebra Banach algebra cohomology Banach bundle Banach bundle...

gives them the structure of a Banach algebra, and in fact they are the standard examples of abelian Von Neumann algebras. The vector space ℓ ∞ {\displaystyle...

║1A║ = 1. Banach algebra Composition algebra Division algebra Gelfand–Mazur theorem Hurwitz's theorem (composition algebras) "Normed Algebra". Encyclopaedia...