PlanetMath: Markov Kakutani fixed point theorem

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Markov Kakutani fixed point theorem

(Theorem)

Theorem [Markov - Kakutani] - Let be a topological vector space and $\mathcal{T}$ a commuting family of continuous linear operators in . Suppose is a compact convex subset of such that

$\displaystyle T(K) \subseteq K$

for every $T \in \mathcal{T}$ . Then there is a point $x_0 \in K$ such that

for all $T \in \mathcal{T}$ .

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Cross-references: point, convex subset, compact, linear operators, continuous, topological vector space

This is version 3 of Markov Kakutani fixed point theorem, born on 2007-09-25, modified 2007-09-25.
Object id is 9963, canonical name is MarkovKakutaniFixedPointTheorem.
Accessed 505 times total.

Classification:

AMS MSC:	46A50 (Functional analysis :: Topological linear spaces and related structures :: Compactness in topological linear spaces; angelic spaces, etc.)
	46A99 (Functional analysis :: Topological linear spaces and related structures :: Miscellaneous)
	54H25 (General topology :: Connections with other structures, applications :: Fixed-point and coincidence theorems)

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