# Questions tagged [oa.operator-algebras]

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

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### Quasinilpotent vectors of Newton potential vanish

Suppose $\Omega$ is a smooth bounded domain in $\mathbb{R}^3$. Consider the Newton potential
\begin{equation}
T [\phi](x) = \int_{\Omega} \frac{1}{|x-y|} \phi(y)dy.
\end{equation}
It is well know ...

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64 views

### Tensor product of compact operators on Banach modules

Let $A$ and $B$ be Banach algebras. Consider a right Banach $A$-module, $E$, and a right Banach $B$-module, $F$, as well as a Banach algebra morphism $\pi\colon A\to\mathcal L_B(F)$ into the bounded $...

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### Relation between spectrum of an operator and its cut down

Let $T$ be a self-adjoint operator in $\mathcal{H}$ with spectrum $\sigma(T)$, Let $P$ be a projection in the commutant of $vN\{T\}$, the von Neumann algebra generated by $T$, question what is the ...

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118 views

### Why are ultraweak *-homomorphisms the `right' morphisms for von Neumann algebras (and say, not ultrastrong)?

Both the ultraweak and ultrastrong topologies are intrinsic topologies in the sense that the image of a continuous (unital) $*$-homomorphism between von Neumann algebras (in either topology) is a von ...

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108 views

### (Noncommutative) Tietze $C^*$ algebras

A unital $C^*$ algebra $A$ is said a Tietze algebra if it satisfies the following:
For every ideal $I$ of $A$ and every unital morphism $\phi: C[0,1] \to A/I$ there is a unital morphism $\tilde{\phi}:...

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### examples of MF algebras [closed]

Can anyone show me concrete examples of unital MF algebra and non-unital MF algebra respectively? Thanks!

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206 views

### Is a set of nuclear functionals equicontinuous in compact-open topology if it is equicontinuous on each compact set?

Let $H$ be a Hilbert space and $B(H)$ be its space of all (bounded) operators. A nuclear functional on $B(H)$ is a linear functional $f:B(H)\to{\mathbb C}$ that can be represented in the form
$$
f(A)=\...

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98 views

### On $s$-numbers in finite von Neumann algebra

$T$ is an operator in $M$, $M$ is finite von Neumann algebra. There is a notion of singular value function that is ($s$-numbers). My question is: what is $s$-number for tensor product of two operators ...

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54 views

### How to find the solution of the equation $b=1+P(ba)$?

We know the solution(commutative case of Spitzer's Identity) of the equation $b=1+\text{P}(ba)$ when the operator $\text{P}$ satisfies Rota-Baxter eqution
$\text{P}(x)\text{P}(y)=\text{P}(x\text{P}(...

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161 views

### Morita equivalence of the invariant uniform Roe algebra and the reduced group C*-algebra

In his paper "Comparing analytic assemby maps", J. Roe considers a proper and cocompact action of a countable group $\Gamma$ on a metric space $X$. He constructs the Hilbert $C^*_r(\Gamma)$-module $L^...

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258 views

### Comparing the definitions of $K$-theory and $K$-homology for $C^*$-algebras

In Higson and Roe's Analytic K-homology, for a unital $C*$-algebra $A$, the definitions of K-theory and K-homology have quite a similar flavor.
Roughly, the group $K_0(A)$ is given by the ...

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148 views

### On diagonal part of tensor product of $C^*$-algebras

Suppose we have a $C^*$-algebra $\mathcal{U}$, Consider the $C^*$-subalgebra generated by elements of the form $a\otimes a$, what is it isomorphic to? Is it isomorphic to $\mathcal{U}$ itself?

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106 views

### Ultraproduct of non-commuative $L^p$-spaces

Let $1<p<\infty.$ Let $I$ be a non-empty set and $\mathcal{U}$ be an ultrafilter over $I.$ Let $M_i$ be von Neumann algebras equipped with normal faithful semifinite traces $\tau_i,$ $i\in I.$ ...

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195 views

### Actions of locally compact groups on the hyperfinite $II_1$ factor

Let $R$ be the hyperfinite $II_1$ factor, and let $G$ be a locally compact group.
(1) Does there always exist a continuous, (faithful) outer action of $G$ on $R$?
(2) If so, how does one ...

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### When does there exist a faithful normal expectation onto von Neumann subalgebra (finite vNa)?

Let $R$ be a finite von Neumann algebra and $S$ be a von Neumann subalgebra of $R$. What conditions must $S$ satisfy so that a faithful normal conditional expectation $\Phi : R \to S$ exists?
For ...