Some Matrix Rearrangement Inequalities

Details Some Matrix Rearrangement Inequalities Some Matrix Rearrangement Inequalities

2004-02-14

arxiv.org/abs/math/0402239v1

Mathematics

Operator Algebras

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Some Matrix Rearrangement Inequalities does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Some Matrix Rearrangement Inequalities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Some Matrix Rearrangement Inequalities will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-179078