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Results tagged with c-star-algebras
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user 763
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: [banach-algebras], [von-neumann-algebras], [operator-algebras], [spectral-theory].
24
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Does left-invertible imply invertible in full group C*-algebras (discrete case)?
The following question/problem has been bugging me on and off for some time now: so I thought it might be worth broaching here on MO, as a case of "ask the experts".
Let $G$ be a discrete group. Kapl …
- 25.8k
20
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Accepted
Are algebraically isomorphic $C^*$-algebras $*$-isomorphic?
Answering the question in the body of the original post, which seems to be more restricted than the implicit question in the title of the post....
The answer is YES. See
L. Terrell Gardner, On is …
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Do torsion-free groups give projectionless group ($C^\ast$) algebras?
Heh, you've picked an open problem: this is the Kadison-Kaplansky conjecture... I would answer it, but first I have to find a sufficiently big margin in which to write the proof.
To be less flippant, …
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16
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$C^*$-algebra generated by those operators that are bounded on every $\ell_p$
Suppose $T: c_{00} \to c_{00}$ is a linear map such that, when regarded as an infinite matrix, there is a uniform bound on the $\ell_1$-norms of its columns, and a uniform bound on the $\ell_1$-norms …
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13
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answer
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What does it tell us, if we know a unital C*-algebra has approximately inner (half-)flip?
This is a somewhat vague question, but I think it is not too open-ended and should admit well-circumscribed answers by specialists in operator algebras.$\newcommand{\Cst}{{\rm C}^*}$ It arises from so …
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11
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2
answers
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Quasinilpotent elements of group C-star algebras
If $G$ is a discrete torsion-free group, can its (reduced or full) group C-star algebra contain non-zero quasinilpotent elements? I've seen various examples in the group von Neumann algebra setting (u …
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11
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Is a C*-algebra with an isomorphic predual a von Neumann algebra?
Via my colleague Garth Dales, some observations which answer your question in the negative, even in the abelian case:$\newcommand{\N}{{\mathbb N}}$
We know that $K$ is hyper-Stonean iff $C(K)$ is …
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10
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Is this a functor on the category of $C^{*}$ algebras?
Here is another attempt at proving no such functor exists — I apologize to Chris and to Manny if something like this is already in the papers which they cite.$\newcommand{\Mat}{{\bf M}}\newcommand{\Cp …
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10
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Quasinilpotent elements of group C-star algebras
Prompted by Douglas Somerset's answer to look harder, I've found a paper of Behncke that also gives what I need, according to MathSciNet, by proving a stronger result:
MR0283582 (44 #813)
Behncke, H. …
10
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Accepted
$K$-theory and surjective norm-decreasing $*$-homomorphisms between $C^*$-algebras
Yes to both.$\newcommand{\Cst}{{\rm C}^*}$
The standard example for the first is: take a discrete group $G$ and let $A$ be its full $\Cst$-algebra, $B$ its reduced $\Cst$-algebra. There is a canonica …
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When are certain group C*-algebras exact?
This is somewhere between a "reference request" and "ask an expert", but I hope it is not too trivial or off-topic.
Anyway. There has been a lot of attention given to showing that for certain discret …
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9
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Is the algebra of compact operators flat?
Assuming that your $\otimes$ denotes min-tensor product of ${\rm C}^\ast$-algebras, then the answer to the question in the body of your post -- which is NOT the same as the question in the title of yo …
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9
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Real rank zero of group $C^*$-algebras
Here is a partial answer, and a pointer towards some literature that should be relevant.$\newcommand{\Cst}{{\rm C}^*}$
Doing some searching online brings up an old result of Kaniuth (Proc. AMS, 1993) …
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The difference between $l^1(G)$ and the reduced group $C^*$ algebra $C_r^*(G)$
A couple of quick comments.
Firstly, I'd advise you to think about what you know about Q1 in the case $G= {\mathbb Z}^d$ (or even just the case $G={\mathbb Z}$) -- because in such settings you can th …
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A precise definition of contractible Banach algebras
$A$ is contractible if $H^1(A,X)=0$ for all Banach $A$-bimodules $X$ (here $H^1$ denotes continuous Hochschild cohomology for Banach algebras, as defined in the works of Johnson or Helemskii). It is a …
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