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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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        votes
        2answers
        79 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 ...
        5
        votes
        1answer
        98 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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        0answers
        87 views

        examples of MF algebras [on hold]

        Can anyone show me concrete examples of unital MF algebra and non-unital MF algebra respectively? Thanks!
        5
        votes
        2answers
        175 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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        0answers
        97 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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        53 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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        votes
        1answer
        143 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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        1answer
        249 views
        +50

        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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        votes
        1answer
        139 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?
        3
        votes
        1answer
        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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        votes
        2answers
        187 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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        0answers
        40 views

        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 ...
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        2answers
        86 views

        Polar decomposition of tensor product of operators in von Neumann algebra

        If $T=V|T|\text { and } S=W|S|$ is the polar decomposition of $T$. Is it true that the polar decomposition of $T\otimes S$ is $T\otimes S=(V\otimes W)(|T| \otimes |S|)$. If $T$ and $S$ are self-...
        2
        votes
        1answer
        81 views

        center of $C^*$-algebra and finite dimensional representation

        The center of $K(H)$ is 0 and $K(H)$ has no nonzero finite dimensional representation. Can we conclude that if the center of a $C^*$-algebra $A$ is zero, then $A$ has no nonzero finite dimensional ...
        3
        votes
        2answers
        136 views

        Ultraweak topology in abelian von Neumann algebras

        Let $A$ be an abelian von Neumann algebra acting on the (not necessarily separable) Hilbert space $\mathcal{H}$ (with identity $I$). From the Gelfand-Neumark theorem, there is a compact Hausdorff ...

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