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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 self-adjoint $a$. So the C*-algebra generated by $a$ need not be commutative either.
19h
comment 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
comment 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 rank-varying operators