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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 oneparameter 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 linebundles tag wiki excerpt 
Nov 15 
reviewed  Approve suggested edit on linebundles 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 preC*algebra. Of course my question was imprecise. Let's ask this: if $V$ is a preHilbert space and $A$ is a selfadjoint 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 preC*algebra? Relevant because a positive answer would answer OP's question. So do we know the answer is negative? 
Nov 14 
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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 preC*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 weightedhomogeneous polynomials 
Nov 14 
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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 
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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 
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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 semicontinuous? 
Oct 17 
reviewed  Reject suggested edit on Estimating the number of clusters 
Oct 5 
reviewed  Approve suggested edit on Group scheme counterexample 