# Questions tagged [oa.operator-algebras]

Algebras of operators on Hilbert space, $C^*-$algebras, von Neumann algebras, non-commutative geometry

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### A locally convex $C^*$ algebra without zero divisor

Let we have a locally convex $C^*$ algebra $A$. That is $A$ is a TVS equipped with an algebra and an involution structure such that all operations are continuous. moreover the topology of $A$ ...
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### Can any POVM be induced by a quantum instrument?

I suspect this is the obvious result of something in operator algebras, but that's far outside my field. Recall that a projection-valued measure is a map $E$ from a sigma-algebra $\mathcal{F}$ on ...
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### 2-positivity to 3-positivity

Let $B\in M_3(\mathbb{C})$ and $S_3= \begin{pmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \\ \end{pmatrix}$. Suppose $I_3\otimes I_2+B\otimes X+B^*\otimes X^*\geq 0$ for all $2$...
148 views

### Semi-commutative von Neumann algebras

Suppose $\Omega$ is a $\sigma$-finite measure space with measure $\mu.$ Let $\mathcal M\subseteq B(H)$ be a von Neumann algebra. Can an element of $L_\infty(\Omega)\overline{\otimes}\mathcal M$ be ...
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### $*$–homomorphisms of the center of $C^*$-algebras

Let $A$ and $B$ be $C^*$-algebras with centers $Z_A$ and $Z_B$. Suppose $\rho：A\rightarrow B$ is a surjective $*$- homomorphism. It is easy to check $\rho(Z_A)\subset Z(B)$. I wonder how to assure ...
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### Decomposition of an element as a difference of positive elements in the definition subalgebra of a weight (Takesaki)

I originally asked this on MSE, but did not get an answer there. Let $M$ be a von Neumann algebra. Let $\varphi: M_+ \to [0, \infty]$ be a weight on $M$. Consider \begin{align*}&\mathfrak{p}_\...
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Let $H$ be a seperable complex Hilbert space. What is the closure of the set of all self adjoint operators in $B(H)$ whose spectrum is a subset of the rational number $\mathbb{Q}$. Apart from finite ...