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visits member for 3 years, 2 months
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Jun
29
comment Shared maximum eigenvector
@DavidHandelman: maybe require $A$ and $B$ to be positive? I'm unsure whether the "maximum" eigenvalue is allowed to be negative ...
Jun
29
comment Shared maximum eigenvector
The question is unclear. Are they real matrices? (Otherwise what do you mean by "largest" --- largest in absolute value?) What kind of condition would you want?
Jun
24
comment An estimate for the maximal C* norm in the group algebra of a free group
You mean "every element of $C[F]$", right? Could you clarify the "it is easy to see" computation. It seems like in the case where $a = a(g)$ for a single $g$ you are saying that the operator norm of a matrix must exceed its trace ... I must be confused about something.
Jun
11
comment Is the Jordan decomposition of a self-adjoint functional constructive?
Mmm, although the proof I have in mind only gets $\phi$ as a difference of positive bounded linear functionals, without the uniqueness or the norm equality.
Jun
11
comment Is the Jordan decomposition of a self-adjoint functional constructive?
It may depend on your definition of C*-algebra. I think I can do this if I know that for every self-adjoint $x \in A$ and $\epsilon > 0$ there is a state $f$ with $f(x) \geq \|x\| - \epsilon$. If C*-algebras are defined concretely as algebras of operators then this is trivial using vector states, but if they are defined abstractly maybe you need Hahn-Banach.
Jun
2
reviewed Approve $\Sigma_1$ elementary substructure
May
24
awarded  Nice Answer
May
13
answered Isometric imbedding of finite metric space into standards spaces
May
4
reviewed Reject riemannian-geometry tag wiki
May
1
answered Banach-Stone Theorem in Lipschitz-free spaces
Apr
23
awarded  Yearling
Apr
20
answered Existence of state on a C*-algebra satisfying $|\tau(ab)|=\|ab\|$
Apr
17
comment Momentum a cotangent vector
@DavidRoberts: I think you're reading something into the question. It looks to me like the OP is just being cautious ...
Apr
8
comment Norm of a matrix operator with a special structure
@Suvrit: it is hard to read "tone" from printed text ... it always surprises me when people can't tell I'm being sarcastic, for example
Apr
8
comment Norm of a matrix operator with a special structure
@Suvrit: it's not positive because it's not self-adjoint.
Mar
30
comment Is $\mathcal{P}(\omega)/fin$ with the interval topology path-connected?
Oh, I misread the definition, sorry.
Mar
30
comment Is $\mathcal{P}(\omega)/fin$ with the interval topology path-connected?
According to your definition of "interval topology", it looks as though every subbasic open set is also closed, in any poset ...
Mar
23
awarded  Nice Answer
Mar
23
comment What are the applications of operator algebras to other areas?
@YemonChoi: +10 for "Atiyah is a dense point in mathematics"
Mar
23
comment What are the applications of operator algebras to other areas?
Huh. No, I haven't encountered this. But no doubt negativity towards other fields is fairly common --- I can be guilty of this myself --- though I suppose I feel it's something one shouldn't take too seriously. That's just human nature.