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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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        (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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        examples of MF algebras [on hold]

        Can anyone show me concrete examples of unital MF algebra and non-unital MF algebra respectively? Thanks!
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        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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        245 views
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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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        138 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
        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 ...
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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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        62 views

        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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        Existence of (generalized) Crossed Products

        Compare the following construction with the crossed product construction for $C^*$-dynamical systems: Let $W\curvearrowright X$ be a group action of a discrete group on a compact Hausdorff space $X$ ...
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        Distributivity of direct sum over maximal tensor product

        Let $A,B$ and $C$ be $C^{*}$-algebras.Does the following identity always holds: $(A \oplus B) \otimes^{max} C \cong (A \otimes^{max}C) \oplus (B \otimes^{max} C)$ My intuition is that this should ...
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        1answer
        122 views

        Need a reference of a fact given in B. Blackadar's Operator Algebras

        I am reading Blackadar's book on Operator algebras. In $\Pi 9.6.5$ Blackader says that Maximal Tensor products commute with arbitrary limits. In the same book the proof of this fact is not given....
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        75 views

        Strictly increasing approximation of the identiy

        Is there always a strictly increasing approximation of the identity in a separable $C^*$-algebra?
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        1answer
        130 views

        Distance between subalgebras and positive elements in matrices

        I repost here from stackexchange, as I was not given an answer there. (https://math.stackexchange.com/questions/2956530/distance-between-subalgebras-and-commutants-in-matrix-algebras) This is a ...
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        75 views

        Real rank 0 implies stable rank 1 on $C^\ast$-algebras?

        A $C^\ast$ algebra has defined stable rank (https://www.univie.ac.at/nuhag-php/bibtex/open_files/2079_Rieffel-StableRank.pdf) and real rank (https://core.ac.uk/download/pdf/82123484.pdf), which are ...

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        山西福彩快乐十分钟
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