field of functional analysis, Banach spaces are among the most important objects of study. In other areas of mathematical analysis, most spaces which...

of the interwar period (1918–1939). Some of the notable mathematical concepts that bear Banach's name include Banach spaces, Banach algebras, Banach measures...

(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...

also References See also: List of Banach spaces, glossary of real and complex analysis. * *-homomorphism between involutive Banach algebras is an algebra...

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...

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...

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...

of topological vector spaces, which include function spaces, inner product spaces, normed spaces, Hilbert spaces and Banach spaces. In this article, vectors...

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...

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...

separable Banach spaces, there is a nice characterization of the precompact sets (in the norm topology) in terms of weakly convergent sequences of functionals:...

topology Hedgehog space Partition topology Zariski topology Counterexamples in Topology – Book by Lynn Steen List of Banach spaces List of fractals by Hausdorff...

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...

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...

taking values in complex Banach spaces (or Fréchet spaces more generally), typically of infinite dimension. It is one aspect of nonlinear functional analysis...

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...

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...

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...

space to be metrizable. Metrizable spaces inherit all topological properties from metric spaces. For example, they are Hausdorff paracompact spaces (and...

{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...

infinite-dimensional normed vector spaces, such as Banach spaces, which resembles the Lebesgue measure used in finite-dimensional spaces. However, the traditional...

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...

Look up Banach in Wiktionary, the free dictionary. Banach (pronounced German pronunciation: ['banax] in German, [ˈbanax] in Slavic Languages, and /ˈbɛnɛk/...

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...

functional analysis and Hilbert space theory, vector-valued Hahn–Banach theorems are generalizations of the Hahn–Banach theorems from linear functionals...

characterization of Hilbert spaces among Banach spaces by S. Kwapień. Using probability in vector spaces, Pisier proved that super-reflexive Banach spaces can be...

Symplectic manifold Banach manifold Fréchet manifold Hilbert manifold List of topological spaces – List of concrete topologies and topological spaces...

theorems Complete space Cauchy sequence Banach fixed-point theorem Polish space Hausdorff distance Intrinsic metric Category of metric spaces Stone duality...

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...

equations) Autonomous convergence theorem (dynamical systems) Banach fixed-point theorem (metric spaces, differential equations) Bendixson–Dulac theorem (dynamical...