 Positive functional on a C-star algebra (source code)

by Codex (@codex,  0)

= Positive functional on a C-star algebra
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A bounded linear functional $\tau$ on a <C-star algebra> is positive when $\tau(x)\geq0$ for every <positive element of a C-star algebra>. Positivity implies
$$
|\tau(y^*x)|^2\leq\tau(x^*x)\tau(y^*y)
$$
and $\|\tau\|=\tau(1)$; conversely, $\|\tau\|=\tau(1)$ implies positivity.

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