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comment Does every commutative $*$-algebra of operators on a prehilbert space have a character?
@Yurii, please post details when you're ready. Sounds interesting.
Nov
18
comment C*-Algebras: Dynamics vs. Derivations
I guess the hint would be that exponentiating the generators should recover the one-parameter groups. The key technical point is that the generators have dense domain, which you can prove using a mollifier.
Nov
16
reviewed Approve suggested edit on surfaces tag wiki excerpt
Nov
15
comment Does every commutative $*$-algebra of operators on a prehilbert space have a character?
@Christian: I don't understand, involution is entrywise complex conjugate? Does this satisfy $\langle Av,w\rangle = \langle v, A^*w\rangle$?
Nov
15
reviewed Approve suggested edit on line-bundles tag wiki excerpt
Nov
15
reviewed Approve suggested edit on line-bundles tag wiki
Nov
15
comment Does every commutative $*$-algebra of operators on a prehilbert space have a character?
@Christian: that's an interesting example, but with appropriate norm your $A$ is a pre-C*-algebra. Of course my question was imprecise. Let's ask this: if $V$ is a pre-Hilbert space and $A$ is a self-adjoint commutative $*$-algebra of linear operators on $V$ (possibly unbounded, with involution in the OP's sense), then is there a norm on $A$ which makes it a pre-C*-algebra? Relevant because a positive answer would answer OP's question. So do we know the answer is negative?
Nov
14
comment Does every commutative $*$-algebra of operators on a prehilbert space have a character?
I'd like to know the answer to this. Do we know that there are such $A$ which are not pre-C*-algebras?
Nov
14
reviewed Approve suggested edit on Standard names and methods for this type of fitting minimization
Nov
14
reviewed Approve suggested edit on Name for generalization of bivariate weighted-homogeneous polynomials
Nov
14
comment Submitting to a mathematics journal for money
Good luck. I'd recommend finding someone you can ask for advice about what would be a suitable venue for publication, once you reach university.
Nov
13
comment Submitting to a mathematics journal for money
... but you deserve an answer. This isn't how it works; the way you earn a living as a research mathematician is by getting a job at a university or in some areas of industry. Generally speaking, you have more freedom to choose what to work on at university, ut you earn more in industry. Well, this is a very short answer that could be made much longer, but the point is that mathematics research isn't typically monetized in the way you seem to think.
Nov
13
comment Submitting to a mathematics journal for money
Kieran, I didn't downvote your question, but I am going to vote to close it because it isn't really appropriate for this website --- we are here to discuss research questions, not "meta" research questions such as yours. (cont.)
Nov
13
comment Strong and weak equivalence of C$^∗$-extensions by compacts
Ah, right. Corrected.
Nov
13
revised Strong and weak equivalence of C$^∗$-extensions by compacts
edited body
Nov
13
answered Strong and weak equivalence of C$^∗$-extensions by compacts
Nov
12
awarded  Civic Duty
Oct
21
reviewed Reject suggested edit on When is fiber dimension upper semi-continuous?
Oct
17
reviewed Reject suggested edit on Estimating the number of clusters
Oct
5
reviewed Approve suggested edit on Group scheme counterexample