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17h

answered  map between $C^*$algebras with special properties, why is $f(a^2)=f(a)^2 $ for all $a\in A$? 
19h

comment 
map between $C^*$algebras with special properties, why is $f(a^2)=f(a)^2 $ for all $a\in A$?
Also, the result is claimed for all $a \in A$, not just selfadjoint $a$. So the C*algebra generated by $a$ need not be commutative either. 
19h

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map between $C^*$algebras with special properties, why is $f(a^2)=f(a)^2 $ for all $a\in A$?
I don't see how we know that the closure of $f(A)$ is commutative  $f$ isn't assumed to be a homomorphism. 
22h

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map between $C^*$algebras with special properties, why is $f(a^2)=f(a)^2 $ for all $a\in A$?
Why can you assume $B = C(Y)$? 
1d

comment 
Separating pure states on the $2\times 2$ matrix algebra
@ChrisRamsey: Sure, although I ultimately will need the stronger result. 
1d

comment 
Separating pure states on the $2\times 2$ matrix algebra
This is really clever, but it doesn't quite work  your characterization of states on $\mathcal{A}'$ is faulty. There are states which aren't vector states. Let $\phi_n$ and $\psi_n$ be the states corresponding to the sequences $(r_1, s_1, \ldots)$ and $(t_1, u_1, \ldots)$ where $r_n = u_n = 1$ and all other terms are zero. Then you see that $\mathcal{B}'$ just barely separates them, so that if $\phi$ and $\psi$ are respectively cluster points of the sequences $(\phi_n)$ and $(\psi_n)$ then $\mathcal{B}'$ doesn't separate $\phi$ and $\psi$. 
Jul 31 
reviewed  Edit almost diagonal Positive semidefinite Matrix 
Jul 31 
revised 
almost diagonal Positive semidefinite Matrix
Lambda (M) and other minor things. 
Jul 31 
reviewed  Approve Zeros of polynomials related to Jensen polynomial associated with Riemann xi function $\xi(x)$ 
Jul 30 
reviewed  Edit History of unstable formulas 
Jul 30 
revised 
History of unstable formulas
added [lo.logic] tag, tried to fix spelling of Ehrenfeucht as well but software called it too minor 
Jul 30 
awarded  Nice Question 
Jul 29 
reviewed  Reject Distributing points evenly on a sphere 
Jul 28 
revised 
Separating pure states on the $2\times 2$ matrix algebra
added 65 characters in body 
Jul 28 
revised 
Separating pure states on the $2\times 2$ matrix algebra
added some motivation and two tags 
Jul 28 
asked  Separating pure states on the $2\times 2$ matrix algebra 
Jul 27 
comment 
Eigenvalues of the sum of two matrices, where one is $B=\operatorname{diag}(1, 0,\dots,0)$
I think @GerryMyerson's comment answers the question, but if you want $A$ to have a nonzero eigenvalue you can take $A = \pmatrix{2&2\cr 1&1}$. Its eigenvalues are $0$ and $1$, but the eigenvalues of $A + B$ are $1 \pm \sqrt{2}$. 
Jul 26 
answered  Hahn Banach type extension of a Lipschitz map 
Jul 25 
comment 
Hahn Banach type extension of a Lipschitz map
The question doesn't make sense  there is no notion of distance in an LCTVS. 
Jul 24 
answered  Continuous section inside a family of rankvarying operators 