mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A {\displaystyle A} over the real or complex...
17 KB (2,606 words) - 03:51, 7 September 2024
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...
103 KB (17,213 words) - 23:33, 24 August 2024
mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties...
20 KB (2,829 words) - 11:21, 17 April 2024
Gelfand representation (redirect from C*-algebra representation)
of representing commutative Banach algebras as algebras of continuous functions; the fact that for commutative C*-algebras, this representation is an isometric...
12 KB (1,817 words) - 16:44, 26 August 2024
that bear Banach's name include Banach spaces, Banach algebras, Banach measures, the Banach–Tarski paradox, the Hahn–Banach theorem, the Banach–Steinhaus...
26 KB (2,699 words) - 18:24, 23 February 2024
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...
19 KB (2,717 words) - 09:00, 4 January 2024
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...
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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)...
3 KB (415 words) - 17:08, 30 November 2021
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...
30 KB (5,658 words) - 21:52, 16 August 2024
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...
44 KB (5,755 words) - 12:46, 8 July 2024
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...
5 KB (545 words) - 03:03, 6 May 2024
Approximate identity (redirect from Σ-unital algebra)
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...
3 KB (474 words) - 21:29, 30 January 2023
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...
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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...
2 KB (310 words) - 14:59, 14 June 2021
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...
2 KB (242 words) - 04:24, 22 June 2022
Normed division algebra Stone–Weierstrass theorem Banach algebra *-algebra B*-algebra C*-algebra Universal C*-algebra Spectrum of a C*-algebra Positive element...
5 KB (475 words) - 23:38, 19 July 2023
\|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...
4 KB (681 words) - 06:07, 10 June 2021
Kaplansky's conjectures (section Banach algebras)
be true in general. This conjecture states that every algebra homomorphism from the Banach algebra C(X) (continuous complex-valued functions on X, where...
8 KB (1,048 words) - 22:08, 28 August 2024
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...
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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)...
27 KB (3,234 words) - 20:46, 8 June 2024
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...
22 KB (2,935 words) - 02:08, 13 August 2024
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...
42 KB (5,905 words) - 00:34, 7 May 2024
Bounded variation (section BV(Ω) is a Banach algebra)
an algebra. This property follows directly from the fact that BV ( Ω ) {\displaystyle \operatorname {\operatorname {BV} } (\Omega )} is a Banach space...
62 KB (8,506 words) - 04:34, 19 July 2024
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...
30 KB (4,256 words) - 13:26, 5 September 2024
ring). *-algebra Affine Lie algebra Akivis algebra Algebra for a monad Albert algebra Alternative algebra AW*-algebra Azumaya algebra Banach algebra Birman–Wenzl...
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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...
2 KB (241 words) - 00:22, 29 June 2022
Operator (mathematics) (category Algebra)
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...
13 KB (1,857 words) - 21:52, 8 May 2024
Banach algebra Amenable Banach algebra Banach Jordan algebra Banach function algebra Banach *-algebra Banach algebra cohomology Banach bundle Banach bundle...
1 KB (125 words) - 15:40, 12 August 2022
L-infinity (category Banach spaces)
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...
5 KB (770 words) - 12:24, 25 June 2024
║1A║ = 1. Banach algebra Composition algebra Division algebra Gelfand–Mazur theorem Hurwitz's theorem (composition algebras) "Normed Algebra". Encyclopaedia...
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