This will display the locations serviced content. This will display the locations serviced content. This will display the locations serviced content.

Demo 1 Logo Demo 1 Logo Club Z!

In-Home & Online Tutoring

Get Math Help

Optional custom content. This can be any HTML containing text, images, links, etc... It will be displayed on all pages!
Demo 1 / Get Math Help

Banach Space

Description

A vector space that possesses a norm which allows computation of vector length and distance between vectors and that is complete in the sense that Cauchy sequences converge.

Relationship graph

Relationship graph

More general classifications

Baire space | barrelled space | bornological space | compactly generated space | complete space | convenient space | Fréchet space | F-space | locally complete space | locally convex space | Mackey space | metrizable space | normed space | pseudo-complete space | pseudo-metrizable space | quasi-Banach space | quasi-barrelled space | quasi-complete space | quasi-normed space | seminormed space | sequentially complete space | stereotype space | topological vector space | webbed space

Examples

A^1(D, dλ^2) | A^2(D, dλ^2) | ℬ(D, dλ^2) | L^∞(T;X) | a^1(D, dλ^2) | a^2(D, dλ^2) | ℬ^h(D, dλ^2) | h^2 | h^∞ | ℬ_0^h(D, dλ^2) | H^2 | H^∞ | L^2(D, dλ^2) | L^∞(D, dλ^2) | ℬ_0(D, dλ^2) | c_0(Z^+, dη) | ℓ^2(Z^+, dη) | ℓ^∞(Z^+, dη)

History

1920 to 1922

Stefan Banach (mathematician)

Hans Hahn | Eduard Helly

Timeline

Timeline

References

Gustave Choquet. Lectures on Analysis. Vol. I: Integration and Topological Vector Spaces. p. 25, 1969. Paul Garrett. "Banach and Fréchet Spaces of Functions." 2014. http://www.math.umn.edu/~garrett/m/fun/notes_2012-13/02_spaces_fcns.pdf. John Horvath. Topological Vector Spaces and Distributions. Vol. I. p. 9, 1966. Taqdir Husain. The Open Mapping and Closed Graph Theorems in Topological Vector Spaces. p. 16, 1965. Taqdir Husain and S.M. Khaleelulla. Barrelledness in Topological and Ordered Vector Spaces. p. 13, 1978. Gottfried Köthe. Topological Vector Spaces. I. p. 126, 1969. Lawrence Narici and Edward Beckenstein. Topological Vector Spaces, 2nd ed. p. 14, 2011. Alexander Provan Robertson and Wendy Robertson. Topological Vector Spaces. p. 60, 1964. Helmut H. Schaefer and Manfred P.H. Wolff. Topological Vector Spaces, 2nd ed. p. 41, 1999. François Trèves. Topological Vector Spaces, Distributions and Kernels. p. 97, 1967. Albert Wilansky. Modern Methods in Topological Vector Spaces. p. 27, 1978. Yau-Chuen Wong. Introductory Theory of Topological Vector Spaces. p. 18, 1992.

Why Club Z!?

We're Awesome!

Vestibulum vitae aliquam nunc. Suspendisse mollis metus ac tellus egestas pharetra. Suspendisse at viverra purus. Pellentesque nec posuere ligula, eu congue leo. Integer vulputate tempor arcu. Vestibulum vulputate

We're Awesome!

Vestibulum vitae aliquam nunc. Suspendisse mollis metus ac tellus egestas pharetra. Suspendisse at viverra purus. Pellentesque nec posuere ligula, eu congue leo. Integer vulputate tempor arcu. Vestibulum vulputate Vestibulum vitae aliquam nunc. Suspendisse mollis metus ac tellus egestas pharetra. Suspendisse at viverra purus. Pellentesque nec posuere ligula, eu congue leo. Integer vulputate tempor arcu. Vestibulum vulputate

We're Awesome!

Vestibulum vitae aliquam nunc. Suspendisse mollis metus ac tellus egestas pharetra. Suspendisse at viverra purus. Pellentesque nec posuere ligula, eu congue leo. Integer vulputate tempor arcu. Vestibulum vulputate Vestibulum vitae aliquam nunc. Suspendisse mollis metus ac tellus egestas pharetra. Suspendisse at viverra purus. Pellentesque nec posuere ligula, eu congue leo. Integer vulputate tempor arcu. Vestibulum vulputate

We're Awesome!

Vestibulum vitae aliquam nunc. Suspendisse mollis metus ac tellus egestas pharetra. Suspendisse at viverra purus. Pellentesque nec posuere ligula, eu congue leo. Integer vulputate tempor arcu.

OUR PURPOSE

We tutor you in the subjects you need to help you progress.

Pre-K Reading Writing Math Science Studdy Skills

Subjects We Tutor

What Is Domain In Math

What Is Domain In Math ‘

Read More...
What Is Domain In Math

What Is Domain In Math ‘

Read More...
Volume of a Sphere

Volume of a Sphere ‘

Read More...
Area of a Triangle

Area of a Triangle ‘

Read More...
Distance Formula

Distance Formula ‘

Read More...
Distance Formula

Distance Formula ‘

Read More...
Volume of a Cylinder

Volume of a Cylinder ‘

Read More...
Find the right fit or it’s free.

We guarantee you’ll find the right tutor, or we’ll cover the first hour of your lesson.