[see also: hope]
Hence we would expect the functions ...... to behave similarly.
We need to check that $F$-derivatives behave in the way we expect with regard to sums, scalar multiples and products.
Compact multipliers, as one would expect, are those elements of $A$ which ......
It seems reasonable to expect that ......, but we have no proof of this.
That is the least one can expect.
There is no reason to expect this to be an inverse map on $K$, but we do have the following.
However, $F$ is only nonnegative rather than strictly positive, as one may have expected.
It will eventually appear that the results are much more satisfactory than one might expect.
Some such difficulty is to be expected.
Along the way, we come across some perhaps unexpected rigidity properties of familiar spaces.