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        Questions tagged [c-star-algebras]

        A C*-algebra is a complex Banach algebra together with an isometric antilinear involution satisfying (a?b)* = b*?a* and the C*-identity ‖a*?a‖ = ‖a‖². Related tags: [tag:banach-algebras], [tag:von-neumann-algebras], [tag:operator-algebras], [tag:spectral-theory].

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        A Banach or $C^*$ algebraic analogy of a classical fact in real analysis

        Let $A$ be a commutative unital Banach algebra.The maximal ideal space of $A$ is denoted by $\hat A$. Assume that $D:A \to A$ is a derivation. Fix an element $a\in A$. Assume that for every $\phi\in \...
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        Closable operators on Hilbert modules

        For $T:{\frak{Dom}}(T) \to H$ a densely defined operator, with $H$ a (separable) Hilbert space, we know that $T$ is closable if its adjoint $T^*$ has dense domain in $H$. Does this extend to the (...
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        Producing $K$-homology cycles from $KK$-cycles

        For two unital (separable) $C^*$-algebras $A$ and $B$, let $(H,\rho,F)$ be a $KK$-cycle in the sense of Kasparov, or in the sense of Wikipedia :) I wonder if there us a natural way to "forget" the ...
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        Complete positivity with infinite dimensional auxillary spaces

        The usual definition of complete positivity (e.g. Stinespring (1955), or Holevo's Statistical Structure of Quantum Theory) is that a linear map between (sub $C^*$ algebras of) the bounded operators on ...
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        multiplier algebra of a simple $C^*$ algebra

        If $A=K(H)$, where $H$ is an infinite dimensional separable Hilbert space, then $A$ is simple and nuclear, and the multiplier algebra $M(A)$ of $A$ is not nuclear. My question is: can we find a non-...
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        Inverse Limit in the category of $C^{\ast}$-algebras or operator spaces

        Does the inverse limits (Projective limits) exist in the category of $C^{\ast}$-algebras or operator spaces? I tried to search but could not find a proper reference. Any reference or comments about ...
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        Restricting functions to an isotropy group

        Let $\mathcal G$ be a locally compact, étale groupoid and let $x$ be a point in the unit space of $\mathcal G$. Writing $\mathcal G(x)$ for the isotropy group at $x$, consider the map $$ f∈C_c(\...
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        (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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        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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        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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        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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        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 ...
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        Is there a non-Kac complex finite dimensional semisimple Hopf algebra?

        A complex (finite-dimensional) Hopf algebra is said to be a Kac algebra if it is a ${\rm C^{\star}}$-algebra in such a way that the comultiplication $\Delta$ is a $\star$-homomorphism. Obviously, a (...
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        A cross product on $C^*_{red} G$

        For every group $G$, the reduced group $C^*$-algebra $C^*_{red}G$ is equipped with the inner product $\langle a,b\rangle=tr(ab^*)$ where "$tr$" is the standard trace on group $C^*$-algebras. For ...
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        representations with centralizer stable under conjugate transpose

        Let $\rho:G\to GL_n(\mathbb{C})$ be a finite-dimensional representation of a finite group $G$ over $\mathbb{C}$, and $C_\rho\subset M_n(\mathbb{C})$ its centralizer, i.e. $m\in C$ iff $m$ commutes ...

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