Banach-Mazur compactum

The Banach-Mazur metric is a distance on the space of all Banach spacesMathworldPlanetmath. If B1,B2 are n-dimensional Banach spaces, the distance between them is


Then d satisfies the triangle inequalityMathworldMathworldPlanetmath, and d(B1,B2)=0 if and only if B1 and B2 are isometric. The space of isometry of n-dimensional Banach spaces under this metric is a compactPlanetmathPlanetmath metric space, known as a Banach-Mazur compactum.

Title Banach-Mazur compactum
Canonical name BanachMazurCompactum
Date of creation 2013-03-22 14:55:24
Last modified on 2013-03-22 14:55:24
Owner bbukh (348)
Last modified by bbukh (348)
Numerical id 5
Author bbukh (348)
Entry type Definition
Classification msc 52A21
Classification msc 46B20
Defines Banach-Mazur metric
Defines Banach-Mazur distance