Timeline for Is Grothendieck classification of tensor norms and Kuratowski's 14 sets theorem somehow related?
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16 events
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| Jan 31, 2014 at 6:41 | vote | accept | Norbert | ||
| Jan 31, 2014 at 1:11 | answer | added | Kevin Beanland | timeline score: 11 | |
| Jan 29, 2014 at 16:18 | comment | added | mathematrucker | This may be offering a tidal wave in response to a request for a glass of water, but there is a comprehensive list of references on the Kuratowski closure-complement theorem at mathtransit.com. | |
| Jan 29, 2014 at 6:08 | comment | added | Will Jagy | And Bhargava showed that there were a total of 14 composition laws Gauss could have chosen for binary quadratic forms. | |
| Jan 28, 2014 at 18:42 | comment | added | Gerhard Paseman | If you do decide to pursue this and write it up, you might find David Sherman's article on variations of the Kuratowski 14-set problem useful. He references a recent paper of Gardner and Jackson which gives other variations and mentions the H,S,P, P_s example of Pigozzi that I mentioned above. Without knowing anything technical about tensor norms, my feeling is that you are dealing with a different semigroup of operators, which might tie in with one of the (partially ordered) semigroups studied in these papers. Gerhard "Ask Me About System Design" Paseman, 2014.01.28 | |
| Jan 28, 2014 at 17:37 | comment | added | Gerhard Paseman | In particular, see if you can find an isomorphism between the two semigroups of operators, even if you can't tell from the relations of the generators. That isomorphism (if it exists) would give you something. Another possibility is that both of them are non-isomorphic subsemigroups of a larger semigroup, which if you found it might reveal more structure of larger classes of objects. Regarding your example, it suggests to me the poset (size 19?) formed by class operators H, S, and P for universal algebraic classes. Gerhard "Promoting The General Algebraic Approach" Paseman, 2014.01.28 | |
| Jan 28, 2014 at 17:30 | comment | added | Gerhard Paseman | Take a look at the relations satisfied by the operators. I don't know about the Grothendieck example, but the topology operators satisfy clcl=cl, ccc=c, cccl=cl and some other equational relationships which I may bother to work out later. Since composition is (usually) associative, in each case you are looking at a (something resembling a) two-generated semigroup which satisfies some relations. If the relations are the same, maybe you have a connection; if they aren't maybe you don't. Gerhard "Or Maybe It Lies Deeper" Paseman, 2014.01.28 | |
| Jan 28, 2014 at 17:14 | history | edited | abx | CC BY-SA 3.0 |
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| Jan 28, 2014 at 17:12 | history | edited | Norbert | CC BY-SA 3.0 |
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| Jan 28, 2014 at 16:46 | comment | added | Norbert | @NateEldredge, in fact, these three norms are included in the list of 14 norms and even more all of them could be derived form only one (see Tensor Norms and Operator Ideals. A. Defant, K. Floret chapter 27) | |
| Jan 28, 2014 at 16:36 | history | edited | Norbert | CC BY-SA 3.0 |
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| Jan 28, 2014 at 16:20 | comment | added | Nate Eldredge | The introduction of the paper you cite speaks of "14 other norms that can be derived from the first 3". So are there 14 or 17? | |
| Jan 28, 2014 at 14:35 | history | edited | Ricardo Andrade |
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| Jan 28, 2014 at 11:17 | comment | added | Norbert | @AlexDegtyarev maybe. I don't know much about operations on tensor norms. | |
| Jan 28, 2014 at 11:00 | comment | added | Alex Degtyarev | Maybe, it's just the idempotence of certain compositions? | |
| Jan 28, 2014 at 10:53 | history | asked | Norbert | CC BY-SA 3.0 |