- #1

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[tex]

\| AB \|_{\mathcal L(X,Z)} \leq \|A\|_{\mathcal L(Y,Z)} \|B\|_{\mathcal L(X,Y)}

[/tex]

It seems like this should be the case, but any time I try to prove a functional analytic result like this, I always get mired in uncertainty about the details...