[see also: call, designate, write, set, symbol, label, relabel, rename]
Denote by $P$ the space of ...... [Not: “Note $P$ the space of ......” or “Denote $P$ the space of ......]
We let $T$ denote the set of ......
......with $e_0$ denoting multiplication by $f$.
The wedge denotes that $e_i$ has been omitted.
Then we can find a subsequence (still denoted by $a_n$) such that $a_n<1$ for all $n$.
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