Logo
Unionpedia
Communication
Get it on Google Play
New! Download Unionpedia on your Android™ device!
Install
Faster access than browser!
 

Fréchet algebra

+ Save concept

In mathematics, especially functional analysis, a Fréchet algebra, named after Maurice René Fréchet, is an associative algebra A over the real or complex numbers that at the same time is also a (locally convex) Fréchet space. [1]

47 relations: Abelian group, Absolutely convex set, Algebra over a field, Associative algebra, Banach algebra, Binomial coefficient, Commutative ring, Compact convergence, Compact space, Complex number, Complex plane, Continuous function, Countable set, Derivative, Differentiable manifold, Dimension, Discrete space, Existential quantification, F-space, Finitely generated group, Fréchet space, Functional analysis, Fundamental theorem of calculus, Gδ set, Group algebra, Holomorphic function, Identity element, Inverse limit, Lebesgue measure, Length function, Locally convex topological vector space, Lp space, Mathematics, Maurice René Fréchet, Monotonic function, N-sphere, Natural number, Neighbourhood (mathematics), Norm (mathematics), Open set, Product rule, Real number, Sequence space, Topological algebra, Uniform convergence, Unit (ring theory), Universal quantification.

Abelian group

In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.

New!!: Fréchet algebra and Abelian group · See more »

Absolutely convex set

A set C in a real or complex vector space is said to be absolutely convex or disked if it is convex and balanced (circled), in which case it is called a disk.

New!!: Fréchet algebra and Absolutely convex set · See more »

Algebra over a field

In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product.

New!!: Fréchet algebra and Algebra over a field · See more »

Associative algebra

In mathematics, an associative algebra is an algebraic structure with compatible operations of addition, multiplication (assumed to be associative), and a scalar multiplication by elements in some field.

New!!: Fréchet algebra and Associative algebra · See more »

Banach algebra

In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers (or over a non-Archimedean complete normed field) that at the same time is also a Banach space, i.e. a normed space and complete in the metric induced by the norm.

New!!: Fréchet algebra and Banach algebra · See more »

Binomial coefficient

In mathematics, any of the positive integers that occurs as a coefficient in the binomial theorem is a binomial coefficient.

New!!: Fréchet algebra and Binomial coefficient · See more »

Christmas

Christmas is an annual festival commemorating the birth of Jesus Christ,Martindale, Cyril Charles.

New!!: Fréchet algebra and Christmas · See more »

Christmas and holiday season

The Christmas season, also called the festive season, or the holiday season (mainly in the U.S. and Canada; often simply called the holidays),, is an annually recurring period recognized in many Western and Western-influenced countries that is generally considered to run from late November to early January.

New!!: Fréchet algebra and Christmas and holiday season · See more »

Christmas Eve

Christmas Eve is the evening or entire day before Christmas Day, the festival commemorating the birth of Jesus.

New!!: Fréchet algebra and Christmas Eve · See more »

Christmas traditions

Christmas traditions vary from country to country.

New!!: Fréchet algebra and Christmas traditions · See more »

Commutative ring

In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative.

New!!: Fréchet algebra and Commutative ring · See more »

Compact convergence

In mathematics compact convergence (or uniform convergence on compact sets) is a type of convergence which generalizes the idea of uniform convergence.

New!!: Fréchet algebra and Compact convergence · See more »

Compact space

In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).

New!!: Fréchet algebra and Compact space · See more »

Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

New!!: Fréchet algebra and Complex number · See more »

Complex plane

In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis.

New!!: Fréchet algebra and Complex plane · See more »

Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

New!!: Fréchet algebra and Continuous function · See more »

Countable set

In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.

New!!: Fréchet algebra and Countable set · See more »

Derivative

The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

New!!: Fréchet algebra and Derivative · See more »

Differentiable manifold

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.

New!!: Fréchet algebra and Differentiable manifold · See more »

Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

New!!: Fréchet algebra and Dimension · See more »

Discrete space

In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points form a discontinuous sequence, meaning they are isolated from each other in a certain sense.

New!!: Fréchet algebra and Discrete space · See more »

Existential quantification

In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some".

New!!: Fréchet algebra and Existential quantification · See more »

F-space

In functional analysis, an F-space is a vector space V over the real or complex numbers together with a metric d: V × V → R so that.

New!!: Fréchet algebra and F-space · See more »

Finitely generated group

In algebra, a finitely generated group is a group G that has some finite generating set S so that every element of G can be written as the combination (under the group operation) of finitely many elements of the finite set S and of inverses of such elements.

New!!: Fréchet algebra and Finitely generated group · See more »

Fréchet space

In functional analysis and related areas of mathematics, Fréchet spaces, named after Maurice Fréchet, are special topological vector spaces.

New!!: Fréchet algebra and Fréchet space · See more »

Functional analysis

Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense.

New!!: Fréchet algebra and Functional analysis · See more »

Fundamental theorem of calculus

The fundamental theorem of calculus is a theorem that links the concept of differentiating a function with the concept of integrating a function.

New!!: Fréchet algebra and Fundamental theorem of calculus · See more »

Gδ set

In the mathematical field of topology, a Gδ set is a subset of a topological space that is a countable intersection of open sets.

New!!: Fréchet algebra and Gδ set · See more »

Group algebra

In mathematics, 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 representations of the algebra are related to representations of the group.

New!!: Fréchet algebra and Group algebra · See more »

Holomorphic function

In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain.

New!!: Fréchet algebra and Holomorphic function · See more »

Identity element

In mathematics, an identity element or neutral element is a special type of element of a set with respect to a binary operation on that set, which leaves other elements unchanged when combined with them.

New!!: Fréchet algebra and Identity element · See more »

Inverse limit

In mathematics, the inverse limit (also called the projective limit or limit) is a construction that allows one to "glue together" several related objects, the precise manner of the gluing process being specified by morphisms between the objects.

New!!: Fréchet algebra and Inverse limit · See more »

Lebesgue measure

In measure theory, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of n-dimensional Euclidean space.

New!!: Fréchet algebra and Lebesgue measure · See more »

Length function

In the mathematical field of geometric group theory, a length function is a function that assigns a number to each element of a group.

New!!: Fréchet algebra and Length function · See more »

Locally convex topological vector space

In functional analysis and related areas of mathematics, locally convex topological vector spaces or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed spaces.

New!!: Fréchet algebra and Locally convex topological vector space · See more »

Lp space

In mathematics, the Lp spaces are function spaces defined using a natural generalization of the ''p''-norm for finite-dimensional vector spaces.

New!!: Fréchet algebra and Lp space · See more »

Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

New!!: Fréchet algebra and Mathematics · See more »

Maurice René Fréchet

Maurice Fréchet (2 September 1878 – 4 June 1973) was a French mathematician.

New!!: Fréchet algebra and Maurice René Fréchet · See more »

Monotonic function

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.

New!!: Fréchet algebra and Monotonic function · See more »

N-sphere

In mathematics, the n-sphere is the generalization of the ordinary sphere to spaces of arbitrary dimension.

New!!: Fréchet algebra and N-sphere · See more »

Natural number

In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

New!!: Fréchet algebra and Natural number · See more »

Neighbourhood (mathematics)

In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space.

New!!: Fréchet algebra and Neighbourhood (mathematics) · See more »

New Year

New Year is the time or day at which a new calendar year begins and the calendar's year count increments by one.

New!!: Fréchet algebra and New Year · See more »

New Year's Day

New Year's Day, also called simply New Year's or New Year, is observed on January 1, the first day of the year on the modern Gregorian calendar as well as the Julian calendar.

New!!: Fréchet algebra and New Year's Day · See more »

New Year's Eve

In the Gregorian calendar, New Year's Eve (also known as Old Year's Day or Saint Sylvester's Day in many countries), the last day of the year, is on 31 December which is the seventh day of Christmastide.

New!!: Fréchet algebra and New Year's Eve · See more »

Norm (mathematics)

In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.

New!!: Fréchet algebra and Norm (mathematics) · See more »

Open set

In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.

New!!: Fréchet algebra and Open set · See more »

Product rule

In calculus, the product rule is a formula used to find the derivatives of products of two or more functions.

New!!: Fréchet algebra and Product rule · See more »

Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

New!!: Fréchet algebra and Real number · See more »

Sequence space

In functional analysis and related areas of mathematics, a sequence space is a vector space whose elements are infinite sequences of real or complex numbers.

New!!: Fréchet algebra and Sequence space · See more »

Topological algebra

In mathematics, a topological algebra A is an algebra and at the same time a topological space, where the algebraic and the topological structures are coherent in a specified sense.

New!!: Fréchet algebra and Topological algebra · See more »

Uniform convergence

In the mathematical field of analysis, uniform convergence is a type of convergence of functions stronger than pointwise convergence.

New!!: Fréchet algebra and Uniform convergence · See more »

Unit (ring theory)

In mathematics, an invertible element or a unit in a (unital) ring is any element that has an inverse element in the multiplicative monoid of, i.e. an element such that The set of units of any ring is closed under multiplication (the product of two units is again a unit), and forms a group for this operation.

New!!: Fréchet algebra and Unit (ring theory) · See more »

Universal quantification

In predicate logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any" or "for all".

New!!: Fréchet algebra and Universal quantification · See more »

2018

2018 has been designated as the third International Year of the Reef by the International Coral Reef Initiative.

New!!: Fréchet algebra and 2018 · See more »

2019

2019 (MMXIX) will be a common year starting on Tuesday of the Gregorian calendar, the 2019th year of the Common Era (CE) and Anno Domini (AD) designations, the 19th year of the 3rd millennium, the 19th year of the 21st century, and the 10th and last year of the 2010s decade.

New!!: Fréchet algebra and 2019 · See more »

Redirects here:

B 0-algebra, B 0-algebras, Frechet algebra, Frechet algebras, Fréchet Algebras, M-convex B 0-algebra, M-convex B 0-algebras, M-convex Frechet algebra, M-convex Frechet algebras.

References

[1] https://en.wikipedia.org/wiki/Fréchet_algebra

OutgoingIncoming
Hey! We are on Facebook now! »