Timeline for Spectral norm and "operator norm" for hypergraphs
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 30, 2021 at 16:33 | comment | added | H A Helfgott | See also mathoverflow.net/questions/388846/… | |
| Mar 30, 2021 at 9:19 | comment | added | H A Helfgott | It seems clear that the same inequality applies when we restrict to functions orthogonal to constant functions (since we are then just working with a vector space of dimension one smaller, and the definitions and inequalities above can be expressed in a coordinate-free way). | |
| Mar 30, 2021 at 9:17 | comment | added | H A Helfgott | Thanks! I didn't find the inequality above as written, but I did find the analogous inequality for the spectral norm $|\mathscr{A}|_\sigma$, which may be defined as $\sup_{\vec{v}\ne 0} |\langle A,\vec{v}^{\otimes k}\rangle|_2/|\vec{v}|_2$: then $|\sum_{S\in E} \prod_{v\in S} f_i(v)| = |\langle A,f_1\otimes \dotsb \otimes f_k\rangle| \leq |\mathscr{A}|_\sigma \prod_{i=1}^k |f_i|_2$. That turns to be an inequality due to Banach. (See also math.tsukuba.ac.jp/~wkbysh/note3.pdf .) | |
| Mar 30, 2021 at 0:44 | comment | added | Suvrit | Did you have a look at a bunch of papers by Shmuel Friedland on the topic of tensor norms and related material? see e.g., ams.org/journals/mcom/2020-89-325/S0025-5718-2020-03525-X/… and also this paper: stat.uchicago.edu/~lekheng/work/nuclear.pdf | |
| Mar 29, 2021 at 23:58 | history | asked | H A Helfgott | CC BY-SA 4.0 |