isometric isomorphism

Let (X,X) and (Y,Y) be normed vector spacesPlanetmathPlanetmath. A surjective linear map T:XY is called an isometric isomorphism between X and Y if

TxY=xX,for allxX.

In this case, X and Y are said to be isometrically isomorphic.

Two isometrically isomorphic normed vector spaces share the same , so they are usually identified with each other.

Title isometric isomorphism
Canonical name IsometricIsomorphism
Date of creation 2013-03-22 17:34:17
Last modified on 2013-03-22 17:34:17
Owner Gorkem (3644)
Last modified by Gorkem (3644)
Numerical id 8
Author Gorkem (3644)
Entry type Definition
Classification msc 46B99
Related topic Isometry
Defines isometrically isomorphic