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12
votes
Are Hilbert-Schmidt operators on separable Hilbert spaces "Hilbert Schmidt" on the space of ...
No it's not.
If $s:H\to H$ is a rank one projection, then
$s\otimes\mathrm{id}:H\otimes \overline H\to H\otimes \overline H$
is a projection of rank $\dim(H)$.
In particular, if $H$ is infinite dime …
6
votes
The definition of unitary fusion category
Given a unitary fusion category, there is more than one natural norm on the (finite dimensional) hom-space $Hom(X,Y)$.
There is the operator norm:
That's the norm under which the unitary fusion categ …