On the Araki-Lieb-Thirring inequality

Details On the Araki-Lieb-Thirring inequality On the Araki-Lieb-Thirring inequality

2007-01-04

arxiv.org/abs/math/0701129v2

Int. J. of Information and Systems Sciences, 4(1), 78-83 (2008)

Mathematics

Functional Analysis

5 pages; accepted version for Intl. J. of Information and Systems Sciences; references added; special issue on "Matrix Analysi

Scientific paper

We prove an inequality that complements the famous Araki-Lieb-Thirring (ALT) inequality for positive matrices $A$ and $B$, by giving a lower bound on the quantity $\trace[A^r B^r A^r]^q$ in terms of $\trace[ABA]^{rq}$ for $0\le r\le 1$ and $q\ge0$, whereas the ALT inequality gives an upper bound. The bound contains certain norms of $A$ and $B$ as additional ingredients and is therefore of a different nature than the Kantorovich type inequality obtained by Bourin (\textit{Math. Inequal. Appl.} \textbf{8}(2005) pp. 373--378) and others. Secondly, we also prove a generalisation of the ALT inequality to general matrices.

Affiliated with

Also associated with

No associations

Rating

On the Araki-Lieb-Thirring inequality 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 On the Araki-Lieb-Thirring inequality, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Araki-Lieb-Thirring inequality will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-310322