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Results tagged with positivity
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user 5690
8
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Hilbert spaces over the semi-field $\mathbb R_+$
Let $\mathbb R_+$ be the semi-field of non-negative real numbers.
Definition (preliminary): A Hilbert space over $\mathbb R_+$ is a pair $(H,P)$, where $H$ is a complex Hilbert space, and $P\subset H …
- 43.2k
8
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Maps which are both completely positive and positive
Definition:A linear map $f:\mathbb C^n\to \mathbb C^n$ is called positive if $\langle fa,a\rangle\ge0$ for all $a\in \mathbb C^n$. Equivalently, $f\in M_{n}(\mathbb C)$ is positive if it can be writte …
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