# Questions tagged [von-neumann-algebras]

Subtag of [tag:oa.operator-algebras] for questions about von Neumann algebras, that is, weak operator topology closed, unital, *-subalgebras of bounded operators on a Hilbert space.

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### Invariance of spectrum under conjugation

Let $T$ be a self-adjoint invertible operator on $\mathcal{H}$ with a continuous spectrum, means the spectral measure is nonatomic. For which class of invertible operators $V$( with continuous ...

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### On commutant of $II_{1}$ factors

Suppose $M$ is $II_{1}$ factor but need not be in standard form. Under what condition (on $M$ or Hilbert space) is the commutant $M'$ of $M$ again $II_{1}$ factor on the Hilbert space acted by $M$?

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### Projections in tensor product of vN algebras

Can we write any projection in the tensor product vN algebra $M\otimes N$ in terms of limits of projections $p\otimes q$, where $p$ and $q$ are projections in M, N or somewhat relate the projections ...

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### On boundedness of sequence of operators in vN algebra

Let $x_{n}$ be a sequence of operators in vN algebra $M$, $\Omega$ is a cyclic vector for $M$, if $x_{n}\Omega$ converges in $\mathcal{H}$, can we say there exist a subsequence $\{y_{n}\}$ of $\{x_{n}\...

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### Separating vector on dense subalgebra

Suppose $M$ be a vN algebra and $U$ be a S.O.T dense self-adjoint subalgebra of $M$ has separating vector, does $M$ have? If not give a counterexample. Or there is a condition on M like type II_{1} or ...

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### A question on standard form in von Neumann algebra

Let $M$ be a vN algebra (represented GNS space with respect to state) in standard form. Under which condition we can say a subalgebra $B$ of $M$ is also in standard form? If there exist $\varphi$ ...

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### Commutant of subalgebra of tensor product

Consider the von Neumann subalgebra of $M\otimes M$ by $ B= \mathrm{vN} \{T\otimes T: T\in M\}$. What is the commutant of B?

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### On cyclicity of fixed point algebra of flip automorphism

Let $M$ be a von Neumann algebra having a cyclic vector in $\mathcal{H}$, is the fixed point subalgebra under the flip automorphism on $M\otimes M$ has a cyclic vector in $\mathcal{H}\otimes \mathcal{...

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### Studying fixed point algebra under group action

If $M$ is in standard form, consider the action of a finite group on $M$, does the fixed point subalgebra under the action is in standard form? What we can say if $M$ is hyperfinite $\mathrm{II}_{1}$ ...

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### Subalgebras of $II_{1}$ factor

Let $M$ be a type $II_{1}$ factor, Let $B$ is an infinite dimensional nonabelian subalgebra. Is it true that $B$ always type $II_{1}$ ?

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### Analogue of spectral values of automorphisms in vN algebra

Is there any analog of studying spectral properties of automorphisms of von Neumann algebra? Does it make sense, if anybody knows please give a reference.

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### Regarding Haagerup $L^{P}$ spaces

There is a definition in Haagerup's paper on $L^{P}$ spaces for weights, my question is after putting the norm is it become semifinite $L^{P}$ space on the crossed product? I am not clear please help. ...

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### 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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### 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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### 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?