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

the term "Banach space" and Banach in turn then coined the term "Fréchet space". Banach spaces originally grew out of the study of function spaces by...

In linear algebra, a sublinear function (or functional as is more often used in functional analysis), also called a quasi-seminorm or a Banach functional...

of representing commutative Banach algebras as algebras of continuous functions; the fact that for commutative C*-algebras, this representation is an isometric...

mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties...

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...

Banach–Stone theorem is a classical result in the theory of continuous functions on topological spaces, named after the mathematicians Stefan Banach and...

\|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...

with the uniform norm). Hence, it is, (by definition) a Banach function algebra. A uniform algebra A on X is said to be natural if the maximal ideals of...

many of the major examples are function spaces carrying a topology; the best known examples include Hilbert spaces and Banach spaces. In functional analysis...

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...

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

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

\}\cup \{1\}} forms a basis for L2[0,1]. Basis (linear algebra) (Hamel basis) Schauder basis (in a Banach space) Dual basis Biorthogonal system (Markushevich...

exponential function makes sense for square matrices (for which the function is called the matrix exponential) and more generally in any unital Banach algebra B...

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...

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...

formalized in universal algebra. Category theory is another formalization that includes also other mathematical structures and functions between structures...

variable réelle". Let X be a Banach space with norm || - ||X. A function f : [0, T] → X is said to be a regulated function if one (and hence both) of the...

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

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...

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

function taking values in a Banach space is a function that equals almost everywhere the limit of a sequence of measurable countably-valued functions...

a Banach algebra, (that is, an associative algebra and a Banach space such that ‖fg‖ ≤ ‖f‖·‖g‖ for all  f, g). The set of all polynomial functions forms...

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...

∈ 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...

In functional analysis, the Hahn–Banach theorem is a central result that allows the extension of bounded linear functionals defined on a vector subspace...

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...