All Questions
Tagged with oa.operator-algebras traces
10 questions
35
votes
2
answers
9k
views
tr(ab) = tr(ba)?
It is well known that given two Hilbert-Schmidt operators $a$ and $b$ on a Hilbert space $H$, their product is trace class and $tr(ab)=tr(ba)$. A similar result holds for $a$ bounded and $b$ trace ...
- 43.2k
9
votes
0
answers
267
views
Can we extend c.p. normal maps on a finite von Neumann algebra $M$ to $L_0(M)_+$?
Suppose that $M$ is a von Neumann algebra with a finite, normal, faithful trace $\tau$. Let $T\colon M\to M$ be a completely positive, normal map.
Can $T$ be extended to a `positively linear map' ...
- 11.3k
7
votes
1
answer
442
views
Completely bounded norm for unital maps with completely positive sections
Consider a completely bounded unital map $\Phi: \mathbf M_h(\mathbb C) \to \mathbf M_k(\mathbb C)$. Suppose that $\Phi$ has right-inverse $\Psi$ which is completely positive. Is the operator norm of $\...
- 1,444
4
votes
1
answer
303
views
Which operators on the trace-class operators extend to operators on Hilbert-Schmidt operators?
Let $\mathcal{H}$ be a separable Hilbert space and let $TC( \mathcal{H})$, $HS(\mathcal{H})$ be the space of trace-class operators and Hilbert-Schmidt operators on $\mathcal{H}$. Recall that these ...
- 1,054
4
votes
1
answer
204
views
Retractions for completely positive unital maps, with particularly nice norms
Consider a non-singular, completely positive, unital map $\Psi: \mathbf M_k(\mathbb C) \to \mathbf M_h(\mathbb C)$. This map will have one or more retractions. Does $\Psi$ admit a retraction $\Phi: \...
- 1,444
3
votes
1
answer
490
views
Bounds on operator 2-norms on partial traces of linearly related operators
Consider an arbitary positive semidefinite operator ρ, acting on ℂA ⊗ ℂB ⊗ ℂC, for A,B,C finite. Also, let P be an orthogonal projector on &#...
- 1,444
3
votes
0
answers
109
views
Faithful traces on reduced $C^*$-algebra of a measured groupoid
Let $G$ be a measured étale groupoid with quasi-invariant measure $\mu$ (that induces the reduced $C^* $-algebra, meaning it has full support) with associated equivalent measures $\nu,\nu^{-1}$.
Is ...
- 261
3
votes
0
answers
160
views
Tensor product of operator subalgebras and properties of the trace
Note that this question was already posted on MSE: https://math.stackexchange.com/questions/4290741/tensor-product-of-operator-subalgebras-and-properties-of-the-trace
Let $V$ be a vector space and let ...
- 139
2
votes
1
answer
195
views
Another formula for the Schwinger term — problems with a calculation
$\DeclareMathOperator\Tr{Tr}$I have a problem with understanding the proof of Proposition 6.8 in the book ,,Elements of Noncommutative Geometry''. One can find the formulation of this proposition here ...
- 9,330
2
votes
1
answer
109
views
Retractions for completely positive unital maps, and their effect on spectral diameter
Consider a non-singular, completely positive, unital map $\Psi: \mathbf M_k(\mathbb C) \to \mathbf M_h(\mathbb C)$. This map will have one or more retractions $\Phi: \mathbf M_h(\mathbb C) \to \mathbf ...
- 1,444