Hence we would expect the functions $f_j$ to behave similarly.
Compact multipliers, as one would expect, are those elements of $A$ which ......
One might hope that this method would work at least for sufficiently regular maps; however, ......
It would clearly have been sufficient to assume ......
If it were true that ......, the same argument would apply to $f$ and would show ......
However, if $B$ were omitted in (1), the case $n=0$ would imply $Nf=1$, an undesirable restriction.
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