Markov Kakutani fixed point theorem

Theorem [Markov - Kakutani] - Let X be a topological vector spaceMathworldPlanetmath and 𝒯 a commuting family of continuous linear operators in X. Suppose K is a compactPlanetmathPlanetmath convex subset of X such that


for every T𝒯. Then there is a point x0K such that Tx0=x0 for all T𝒯.

Title Markov Kakutani fixed point theorem
Canonical name MarkovKakutaniFixedPointTheorem
Date of creation 2013-03-22 17:33:25
Last modified on 2013-03-22 17:33:25
Owner asteroid (17536)
Last modified by asteroid (17536)
Numerical id 6
Author asteroid (17536)
Entry type Theorem
Classification msc 54H25
Classification msc 46A99
Classification msc 46A50