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The Cauchy-Schwarz inequality states $|\langle x,y \rangle |\leq ||x||\cdot ||y||.$ Use this tag for questions related to the CS inequality and its applications.

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Does the Cauchy–Schwarz inequality imply 2-positivity?

Recall the following generalisation of Cauchy–Schwarz. Theorem. Let $f\colon \mathscr{A} \to \mathscr{B}$ be a linear 2-positive map between C$^*$-algebras. Then for all $a,b \in \mathscr{A}$ we …