field of functional analysis, Banach spaces are among the most important objects of study. In other areas of mathematical analysis, most spaces which...
2 KB (449 words) - 23:44, 26 July 2024
of the interwar period (1918–1939). Some of the notable mathematical concepts that bear Banach's name include Banach spaces, Banach algebras, Banach measures...
27 KB (2,751 words) - 05:54, 29 May 2025
(Riesz 1910). Lp spaces form an important class of Banach spaces in functional analysis, and of topological vector spaces. Because of their key role in...
65 KB (12,217 words) - 21:17, 14 April 2025
also References See also: List of Banach spaces, glossary of real and complex analysis. * *-homomorphism between involutive Banach algebras is an algebra...
22 KB (3,264 words) - 05:29, 7 June 2025
spaces is the Hahn–Banach theorem. The definition of many normed spaces (in particular, Banach spaces) involves a seminorm defined on a vector space and...
18 KB (2,881 words) - 18:43, 8 May 2025
is a list of vector spaces in abstract mathematics, by Wikipedia page. Banach space Besov space Bochner space Dual space Euclidean space Fock space Fréchet...
675 bytes (54 words) - 17:59, 16 March 2022
of the space of countably additive μ-a.c. bounded measures inside the space of all finitely additive μ-a.c. bounded measures. List of Banach spaces Dunford...
6 KB (876 words) - 18:38, 18 August 2024
of topological vector spaces, which include function spaces, inner product spaces, normed spaces, Hilbert spaces and Banach spaces. In this article, vectors...
87 KB (11,491 words) - 02:01, 5 June 2025
Hilbert space – Type of vector space in math List of Banach spaces List of topologies – List of concrete topologies and topological spaces Metric space#Open...
3 KB (512 words) - 12:16, 28 March 2024
infinite-dimensional spaces Stefan Banach (1892–1945) Hugo Steinhaus (1887–1972) John von Neumann (1903-1957) Alain Connes (born 1947) Earliest Known Uses of Some of the...
5 KB (475 words) - 23:38, 19 July 2023
separable Banach spaces, there is a nice characterization of the precompact sets (in the norm topology) in terms of weakly convergent sequences of functionals:...
14 KB (1,935 words) - 11:37, 6 May 2025
topology Hedgehog space Partition topology Zariski topology Counterexamples in Topology – Book by Lynn Steen List of Banach spaces List of fractals by Hausdorff...
15 KB (2,036 words) - 16:26, 1 April 2025
branches of mathematics, the Banach–Alaoglu theorem (also known as Alaoglu's theorem) states that the closed unit ball of the dual space of a normed vector...
61 KB (8,306 words) - 04:30, 25 September 2024
Sublinear function (category CS1 maint: multiple names: authors list)
quasi-seminorm or a Banach functional, on a vector space X {\displaystyle X} is a real-valued function with only some of the properties of a seminorm. Unlike...
22 KB (4,192 words) - 17:21, 18 April 2025
Infinite-dimensional holomorphy (redirect from Banach space of analytic functions with infinite-dimensional domains)
taking values in complex Banach spaces (or Fréchet spaces more generally), typically of infinite dimension. It is one aspect of nonlinear functional analysis...
9 KB (1,358 words) - 16:52, 18 July 2024
g(x)){\text{.}}} Examples of non-lattice Banach spaces are now known; James' space is one such. The continuous dual space of a Banach lattice is equal to its...
4 KB (466 words) - 02:33, 27 February 2024
subset of the parent space which retains the same structure. While modern mathematics uses many types of spaces, such as Euclidean spaces, linear spaces, topological...
69 KB (9,328 words) - 07:29, 5 June 2025
line, any separable Banach space, the Cantor space, and the Baire space. Additionally, some spaces that are not complete metric spaces in the usual metric...
12 KB (1,509 words) - 21:41, 29 May 2025
space to be metrizable. Metrizable spaces inherit all topological properties from metric spaces. For example, they are Hausdorff paracompact spaces (and...
7 KB (865 words) - 19:15, 10 April 2025
{S}}'(\mathbb {R} ).} Another example is given by Sobolev spaces: Here (in the simplest case of Sobolev spaces on R n {\displaystyle \mathbb {R} ^{n}} ) H = L 2...
8 KB (1,016 words) - 07:18, 12 January 2025
Infinite-dimensional Lebesgue measure (category Banach spaces)
infinite-dimensional normed vector spaces, such as Banach spaces, which resembles the Lebesgue measure used in finite-dimensional spaces. However, the traditional...
7 KB (1,035 words) - 03:08, 20 April 2025
Functional analysis (section Banach spaces)
class of spaces studied in functional analysis are complete normed vector spaces over the real or complex numbers. Such spaces are called Banach spaces. An...
20 KB (2,496 words) - 21:48, 29 April 2025
Look up Banach in Wiktionary, the free dictionary. Banach (pronounced German pronunciation: ['banax] in German, [ˈbanax] in Slavic Languages, and /ˈbɛnɛk/...
4 KB (408 words) - 07:11, 19 February 2025
Hausdorff spaces are also called T2 spaces. The name separated space is also used. A related, but weaker, notion is that of a preregular space. X {\displaystyle...
16 KB (2,156 words) - 02:43, 25 March 2025
functional analysis and Hilbert space theory, vector-valued Hahn–Banach theorems are generalizations of the Hahn–Banach theorems from linear functionals...
9 KB (1,208 words) - 07:53, 3 July 2023
Gilles Pisier (category Academic staff of the University of Paris)
characterization of Hilbert spaces among Banach spaces by S. Kwapień. Using probability in vector spaces, Pisier proved that super-reflexive Banach spaces can be...
9 KB (794 words) - 14:45, 12 March 2025
Symplectic manifold Banach manifold Fréchet manifold Hilbert manifold List of topological spaces – List of concrete topologies and topological spaces...
4 KB (287 words) - 19:11, 15 September 2022
theorems Complete space Cauchy sequence Banach fixed-point theorem Polish space Hausdorff distance Intrinsic metric Category of metric spaces Stone duality...
5 KB (401 words) - 16:43, 1 April 2025
topological vector space is a set that is convex, balanced, absorbing, and closed. Barrelled spaces are studied because a form of the Banach–Steinhaus theorem...
23 KB (3,555 words) - 08:56, 1 June 2025
equations) Autonomous convergence theorem (dynamical systems) Banach fixed-point theorem (metric spaces, differential equations) Bendixson–Dulac theorem (dynamical...
78 KB (6,289 words) - 12:34, 6 June 2025