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In the question Prove that projection operator is non-expansive, the author wants to prove that an operator is non-expansive. In the context of reinforcement learning, I heard that the $\max$ and $\min$ operators are non-expansive.

But what exactly is a non-expansive operator? What is the definition of an non-expansive operator? Why exactly exactly a max is non-expansive?

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Non-expansive means:

$$ \| P(x) - P(y) \| \leq L \| x - y \|$$

for some norm in questions and $L \leq 1$.

Note: Of course this can be generalize for distances, metric spaces and probably even topologies.

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