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# Questions tagged [oa.operator-algebras]

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

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0answers
60 views

### Radon-Nikodym derivatives in von Neumann algebra

Let $\mathcal M$ be a noncommutative probability space i.e. there is a trace $tau$ on $\mathcal M$ such that it is normal, faithful and $\tau(1)=1.$ Let $\tau_1$ be a normal trace on $\mathcal M$. ...
0answers
51 views

### type III$_1$ states

Given a von Neumann algebra that is a type III$_1$ factor with the state $\omega$ and any $\epsilon>0$ is it always possible to find a projection or a partial isometry in the algebra such that its ...
0answers
26 views

### Converegence of modulus in nocommutative $L_p$-spaces

Let $1\leq p<\infty.$ Let $\mathcal M$ be a von Neumann algebra equipped with a normal semifinite faithful trace $\tau.$ Let $L_p(\mathcal M,\tau)$ be the associated noncommutative $L_p$-space. Let ...
1answer
70 views

### Graded adjointable operators on a graded Hilbert space

Given a graded Hilbert space $\mathbf{H} = \bigoplus_{k \in \mathbb{N}} \mathbf{H}_k$, one might extend the notion of adjoint to a "graded adjoint" defined as follows: $L \in B(\mathbf{H})$ is said to ...
1answer
75 views

0answers
95 views

### Can every dynamical system be interpreted in terms of (unitary) conjugation in an operator algebra

Let $H$ be a Hilbert space and $X$ be a compact Hausdorff space with a homeomorphism $\alpha: X \to X$. Assume that $C(X)$ is a commutative sub algebra of $B(H)$, namely $C(X)$ is embedded in $B(H)$...
0answers
70 views

### Invertibility modulo the intersection of ideals in $C^*$-algebras

This is a crosspost from math.se because it did not get any attention whatsoever. I therefore assume that it fits here better. Let $\mathcal{A}$ be a $C^*$-algebra and $A \in \mathcal{A}$. I am ...
1answer
165 views

### Quantum (group) version of ${\mathbb Z}^n$?

As we know there are quantum analogue of tori called quantum tori generated by noncommuting operators $(A_1,\dots,A_n)$ with $A _iA_j=A_jA_ie^{2\pi i\alpha}$ where $\alpha$ is a irrational number as a ...
1answer
119 views

### Does the square root of a finite propagation operator have finite propagation?

Let $X$ be a non-compact manifold and let $C_0(X)$ act on $L^2(X)$ by pointwise multiplication. We say $T\in\mathcal{B}(L^2(X))$ has finite propagation if there exists an $r>0$ such that: for all ...
2answers
164 views

### $2$-norm distance between square roots of matrices

Suppose two square real matrices $A$ and $B$ are close in the Schatten 1-norm, i.e. $\|A-B\|_1=\varepsilon$. Can this be used to put a bound on the Schatten 2-norm distance between their square roots. ...
1answer
76 views

### Tensoring adjointable maps on Hilbert modules

Given a right Hilbert $A$-module $E$, and a right Hilbert $B$-module $F$, together with non-degenerate $*$-homomorphism $\phi:A \to \mathcal{L}_B(F)$, we can form the tensor product  E \otimes_{\phi}...
1answer
73 views

### Normal $*$-homomorphism

Let $\pi:\mathscr M\to\mathscr M$ be a normal $*$-homomorphism between a von Neumann algebra $\mathscr M.$ Assume $\mathscr M$ has a normal semifinite faithful trace. Does $\pi$ extend as a bounded ...
0answers
32 views

### On weakly equivalent actions

If $G\curvearrowright (X,\mu)$ and $G\curvearrowright (Y,\nu)$ are weakly equivalent pmp actions(standard definition in literature),( where $G$ is discrete group and $\mu$, $\nu$ are probability ...

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