Timeline for which norms can be realized as operator norms?
Current License: CC BY-SA 3.0
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| Jun 6, 2015 at 21:50 | comment | added | Asaf Shachar | Yes, but the Frobenius norm is induced by an inner product. As I stated in the question, we already know that (except for trivial dimensions) these kind of norms cannot be realized as operator norms. For all we know, all norms that come from inner products satisfy the condition Denis suggested, so the space of optional candidates for realization does not really decrease. Saying it differently, I want to make sure Denis's condition is indeed restrictive. | |
| Jun 4, 2015 at 12:57 | comment | added | Jean Van Schaftingen | This condition is satisfied by the Frobenius/Hilbert-Schmidt norm which seems not to be an operator norm. There should be another obstruction hanging around. | |
| Jun 4, 2015 at 10:28 | history | edited | Denis Serre | CC BY-SA 3.0 |
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| Jun 4, 2015 at 10:24 | comment | added | Asaf Shachar | You are right. Do you see immediately that ypur additional constraint really decreases the space of possible realizable norms? i.e is it trivial to find a norm which is not induced by inner product, and does not satisfy this requirement. such a norm will be outside the realizable space. | |
| Jun 4, 2015 at 10:15 | history | answered | Denis Serre | CC BY-SA 3.0 |