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Uniform algebra

In functional analysis, a uniform algebra A on a compact Hausdorff topological space X is a closed (with respect to the uniform norm) subalgebra of the C*-algebra C(X) (the continuous complex-valued f

Noncommutative topology

In mathematics, noncommutative topology is a term used for the relationship between topological and C*-algebraic concepts. The term has its origins in the Gelfand–Naimark theorem, which implies the du

Shilov boundary

In functional analysis, a branch of mathematics, the Shilov boundary is the smallest closed subset of the structure space of a commutative Banach algebra where an analog of the maximum modulus princip

Banach algebra cohomology

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 cohomology of an abstract algebra, except th

Approximate identity

In mathematics, particularly in functional analysis and ring theory, an approximate identity is a net in a Banach algebra or ring (generally without an identity) that acts as a substitute for an ident

Gelfand representation

In mathematics, the Gelfand representation in functional analysis (named after I. M. Gelfand) is either of two things:
* a way of representing commutative Banach algebras as algebras of continuous fu

Corona theorem

In mathematics, the corona theorem is a result about the spectrum of the bounded holomorphic functions on the open unit disc, conjectured by and proved by Lennart Carleson. The commutative Banach alge

Banach function algebra

In 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, complex-valued functions from X, togethe

Wiener algebra

In mathematics, the Wiener algebra, named after Norbert Wiener and usually denoted by A(T), is the space of absolutely convergent Fourier series. Here T denotes the circle group.

Disk algebra

In mathematics, specifically in functional and complex analysis, the disk algebra A(D) (also spelled disc algebra) is the set of holomorphic functions ƒ : D → , (where D is the open unit disk in the c

Gelfand–Mazur theorem

In operator theory, the Gelfand–Mazur theorem is a theorem named after Israel Gelfand and Stanisław Mazur which states that a Banach algebra with unit over the complex numbers in which every nonzero e

Index group

In operator theory, a branch of mathematics, every Banach algebra can be associated with a group called its abstract index group.

Banach algebra

In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra over the real or complex numbers (or over a non-Archimedean complete ) that at th

Cohen–Hewitt factorization theorem

In mathematics, the Cohen–Hewitt factorization theorem states that if is a left module over a Banach algebra with a left approximate unit , then an element of can be factorized as a product (for some

Amenable Banach algebra

In mathematics, specifically in functional analysis, a Banach algebra, A, is amenable if all bounded derivations from A into dual are (that is of the form for some in the dual module). An equivalent c

Sherman–Takeda theorem

In mathematics, the Sherman–Takeda theorem states that if A is a C*-algebra then its double dual is a W*-algebra, and is isomorphic to the weak closure of A in the universal representation of A. The t

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