I had asked this question here but received no answer.
Let $O$ be an operator that maps sequences to sequences such that the elements of the sequence $O(a)$ are given by
$$\bigl(O(a)\bigr)_n ~{}={}~ \sup_{k \geq n}\, a_k~.$$
$O(a)$ should be the tightest monotonically decreasing sequence that dominates $a$.
Is there a name for $O$ or for $O(a)$? In other words: Is there terminology for the tightest monotonically decreasing majorant of a sequence? Or alternatively terminology for a very related/similar object?
Dually, I am looking for a name where $O$ uses $\inf$ instead of a $\sup$.
