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        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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        113 views

        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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        1answer
        82 views

        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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        36 views

        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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        1answer
        81 views

        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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        45 views

        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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        1answer
        125 views

        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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        1answer
        118 views

        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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        48 views

        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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        48 views

        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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        1answer
        98 views

        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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        1answer
        61 views

        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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        2answers
        153 views

        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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        2answers
        138 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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        116 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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        1answer
        173 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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