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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].
1
vote
A variant of the Stone-Weierstrass theorem?
EDIT 20-03-12 It seems from the recent answers of Douglas Somerset and Ulrich Pennig that what I claim below is false, and so this answer should be "dis-accepted".
I think (although I admit I don't …
- 25.8k
2
votes
Suppose that $a \mu = \mu a$ for all $a$ in $C^*$-algebra $A$. Then $\mu \in Z(A^{**})$
I think this follows from the fact that multiplication in $A^{**}$ is separately weak-star continuous, i.e.
for all $a\in A^{**}$ the function $A^{**} \to A^{**}$, $b\mapsto ab$, is weak-star to weak …
- 25.8k
9
votes
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 …
- 25.8k
1
vote
Is the algebra of bounded operators stable?
In response to Matt "calling my bluff" I realised that my claim takes some work to justify. The following is very much "thinking aloud through a head cold" so is not a polished exposition, and I have …
- 25.8k
24
votes
2
answers
1k
views
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
10
votes
Accepted
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 …
- 25.8k
2
votes
$id:A\to A^{op}$ is completely positive iff $A$ is abelian
I'm not sure where I saw the following argument: it might have been mentioned in a book, or a paper, or a lecture.
I seem to remember that every non-abelian ${\rm C}^*$-algebra contains a *-subalgebr …
- 25.8k
5
votes
1
answer
177
views
Hopf C-star algebra/comodules using a Fubini tensor product rather than the minimal tensor p...
Throughout, $\otimes$ denotes the minimal tensor product of $\newcommand{\Cst}{{\rm C}^{\ast}}\Cst$-algebras. and $\odot$ denotes the tensor product of (underlying) vector spaces.
Given two $\Cst$-al …
- 25.8k
5
votes
1
answer
284
views
A perturbation question for the intersection of C*-subalgebras
This feels like something I may have asked before (in which case, apologies) and it also might be some kind of "standard counterexample in a book on C* algebras".
Let M be a unital C*-algebra and let …
- 25.8k
10
votes
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. …
3
votes
Accepted
Existence of an integrable representation
[Thanks to Loren Spice for fixing the references and pointing out a silly error/mis-statement in the original version of this answer.]
The answer to Q1 is no for $G={\mathbb Z}$, since all its irre …
- 25.8k
20
votes
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 …
- 25.8k
4
votes
center of a $C^*$-algebra
I think you can obtain an example by modifying the classical Toeplitz algebra.
$\newcommand{\H}{\mathbf{H}}$
$\newcommand{\bT}{\mathbf{T}}$
$\newcommand{\cT}{\mathcal T}$
$\newcommand{\KH}{{\mathcal …
- 25.8k
11
votes
2
answers
630
views
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 …
- 25.8k
13
votes
1
answer
298
views
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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