Proof that that maximal and minimal $C^{*}$ tensor norms are actually 'largest' and 'smallest' norms?

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I'm looking for the proof of the following theorem, and can't seem to find one online that's accessible (as in, it's behind a paywall or perhaps buried in some paper).

Theorem: Let $A,B$ be $C^{*}$ algebras. Then the maximal and minimal norms $||\cdot||_{\max}$ and $||\cdot||_{\min}$ respectively on the algebraic tensor $A \odot B$ are the largest and smallest $C^{*}$ norms on $A \odot B$.

This seems maybe somewhat obvious from their names, but I was wondering if the proof was available somewhere to look at. From looking online, it seems that it's located in "M. Takesaki: Theory of Operator Algebras I, Springer, 2001" but that's locked behind a paywall.

If anyone could provide a link, that'd be extremely helpful!