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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Message
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| Hello,
in:
"The converse is also true, although it is not so simple to prove. Indeed,
Theorem - $ T$ is positive if and only if $ \langle Tv, v \rangle \geq 0 \;\;\;\;\forall_{v \in H}$"
do you assume that T is self-adjoint in the first place, so that <Tv,v> is real (and can therefore be compared to 0)? Or do you mean that [<Tv,v> is real and nonnegative] implies positivity for arbitrary T? (the latter sounds rather strong) |
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