Since $f$ is compact, we have $Lf=0$.
Since $f$ is compact, it follows that $Lf=0$. [Not: “Since $f$ is compact, then $Lf=0$.”]
[In sentences beginning with Since, it is sometimes unclear which part is the premise, and which is the conclusion: instead of writing: “Since $A=B$, $B=C$, $C=D$, $A=C$”, write e.g.: Since $A=B$ and $B=C$, and since moreover $C=D$, it follows that $A=C$.]
The argument is a variant of one in [5] and has been used several times since.
There has since been a series of improvements, of which we briefly mention the work of Levinson.
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