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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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      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 $\mathcal M$. ...
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      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 ...
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      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 ...
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      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 ...
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      1answer
      75 views

      Extending $C^*$-norms from $*$-subalgebras

      Let $A$ be a unital $*$-algebra, and $B$ a unital $*$-subalgebra of $A$. In addition, assume that there exists a $B$-$B$-sub-bimodule $C \subset A$, such that $$ A \simeq B \oplus C, $$ where $\...
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      57 views

      Commutative subalgebras of $B(H)$ whose all automorphisms are in the form of unitary conjugation

      Let $H$ be a complex Hilbert space. Is there a compact Hausdorff space $X$ such that $C(X)$ is embeded in $B(H)$ and for every homeomorphism $\alpha$ of $X$ there exist a unitary operator $u\in B(H)$ ...
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      72 views

      On standard form of corners

      Let $(M, \tau)$ be a $\mathrm{II_{1}}$ factor equipped with the faithful normal tracial state $\tau$ acts on $L^{2}(M,\tau)$ is in standard form. The question is: if we consider vN algebras $PMP(P\in ...
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      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 $B(H)$...
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      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 ...
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      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 ...
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      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 ...
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      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. ...
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      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}...
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      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 ...
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      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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