Some Matrix Rearrangement Inequalities
| dc.creator | Carlen, Eric | |
| dc.creator | Lieb, Elliott H. | |
| dc.date | 2004-02-14 | |
| dc.date.accessioned | 2026-07-07T05:05:27Z | |
| dc.date.available | 2026-07-07T05:05:27Z | |
| dc.description | We investigate a rearrangement inequality for pairs of n-square matrices: Let |A\|_p denote the C^p trace norm of an n-square matrix A. Consider the quantity |A+B|_p^p + |A-B|_p^p. Under certain positivity conditions, we show that this is nonincreasing for a natural ``rearrangement'' of the matrices A and B when 1 \le p \le 2. We conjecture that this is true in general, without any restrictions on A and B. Were this the case, it would prove the analog of Hanner's inequality for L^p function spaces, and would show that the unit ball in C^p has the exact same moduli of smoothness and convexity as does the unit ball in L^p for all 1 < p < \infty. At present this is known to be the case only for 1 < p \le 4/3, p =2, and p\ge 4. Several other rearrangement inequalities that are of interest in their own right are proved as the lemmas used in proving the main results. | |
| dc.identifier | https://arxiv.org/abs/math/0402239 | |
| dc.identifier | http://arxiv.org/abs/math/0402239 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70171 | |
| dc.subject | Operator Algebras | |
| dc.subject | Mathematical Physics | |
| dc.subject | Rings and Algebras | |
| dc.subject | 15A45; 15A18; 15A42; 47A30; 47A63 | |
| dc.title | Some Matrix Rearrangement Inequalities | |
| dc.type | text |