Timeline for Norm on quotient algebra of a tensor algebra
Current License: CC BY-SA 2.5
8 events
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| Jan 24, 2010 at 1:46 | comment | added | Jonas Meyer | You are welcome to e-mail me (although I make no promises of time to think about this). But it is also typically considered reasonable, even encouraged, to add background to your question. In this case, I would think that people could better understand your problem if we knew what computing problem you are modeling, so it wouldn't be off topic to add that in my opinion. | |
| Jan 24, 2010 at 1:15 | comment | added | Daoud | They could well do. The application is a very practical one in computing. The specific properties of the vector space are up for grabs - the main requirement is simply that we can compute the norm on the quotient algebra. If you're interested, perhaps we could discuss this via email, as I have a feeling we may have to go off-topic (I found your home page). Thanks again for your help. | |
| Jan 23, 2010 at 23:44 | comment | added | Jonas Meyer | There is a reason I called that part of my answer "gratuitous". The construction came to mind and I couldn't resist mentioning it, but I had no reason to think it would have bearing on solving your problem. But perhaps the translated problem(s) would interest you too? | |
| Jan 23, 2010 at 23:37 | comment | added | Jonas Meyer | I don't know a good reference for discussing this phenomenon in general, but the problem is this: Your problem is about a purely algebraic object, Q. If you translate the problem to a functional analysis problem (and it is not even clear to me what the best way to do that is), then it is a different problem that may not help you in your original problem. If you could find a way to embed Q faithfully in a quotient Banach algebra then you would get a norm, but this won't always be possible because in the Banach algebra quotient you mod out by a bigger ideal (that is the problem of closing). | |
| Jan 23, 2010 at 23:10 | comment | added | Daoud | I'm afraid I didn't understand this part of your answer (I must confess I'm not a mathematician). Perhaps you could point me to a reference that would help me understand why closing causes such a problem. | |
| Jan 23, 2010 at 23:06 | comment | added | Jonas Meyer | I don't see why you would necessarily want to throw in the annihilation operators; couldn't you work in non-self-adjoint algebras rather than C* algebras? In either case, to have a Banach algebra norm on the quotient you will need to close your tensor algebra and ideal, and I do not see how this will relate directly to the orginal construction. | |
| Jan 23, 2010 at 22:31 | history | edited | Daoud | CC BY-SA 2.5 |
Exchange link that didn't work with a proper reference.
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| Jan 23, 2010 at 22:23 | history | answered | Daoud | CC BY-SA 2.5 |