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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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      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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      66 views

      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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      90 views

      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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      1answer
      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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      1answer
      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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      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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      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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      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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