# Tagged Questions

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### Reference request for the proof of the Brodskii–Milman fixed point theroem for isometries

Can any one help me to access the paper M.S Brodskii and D.P Milman, On the center of a convex set, Dokl. Akad. Nauk SSSR 59 (1948) 837–840 in Russian? or to prove the theorem If $K$ is a ...
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### Reference request: result concerning Leray trace

Let $V$ be a vector space (possibly of infinite dimension). For a linear homomorphism $f\colon V\to V$ define N(f)=\bigcup_{n\in\mathbb{N}} \operatorname{ker}(\underbrace{f\circ\ldots\circ ...
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### Banach Fixed Point Theorem. Measurable version.

The Banach fixed point theorem has the following statement THEOREM ( Banach contraction principle). Let $(Y,d)$ be a complete metric space and $F:Y\to Y$ be contractive . Then $F$ has a uniqe ...
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### Fixed point of matrix

Suppose that $a$ is a fixed point of matrix $A$, what that means? What is a fixed point of matrix? Thank you!
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### Question about Fixed Point Theorem Hypotheses

Consider the following (less general than possible) statement of Schauder's fixed point theorem: Suppose that $X$ is a Banach space, that $B_1$ is the unit ball of $X$ and that $f: X \to X$ is a ...
Let $X$ be a Borel space with a Borel measure $\mu$. Suppose $\xi: X\times X\to\mathbb R_{\geq 0}$ is a continuous function and put $s(x) = \{y\in X:\xi(x,y) = 0\}$. For any set $b\in\mathcal B(X)$ we ...