JIPAM

On Chaotic Order of Indefinite Type  
 
  Authors: Takashi Sano,  
  Keywords: Chaotic order; (Indefinite) Inner product space; Furuta inequality of indefinite type.  
  Date Received: 02/06/06  
  Date Accepted: 27/04/07  
  Subject Codes:

47B50, 47A63.

  
  Editors: Frank Hansen,  
 
  Abstract:

Let $ A, B$ be $ J$-selfadjoint matrices with positive eigenvalues and $ I geqq^J A, I geqq^J B.$ Then it is proved as an application of Furuta inequality of indefinite type that

$displaystyle mathrm{Log} A geqq^J mathrm{Log} B $
if and only if
$displaystyle A^r geqq^J (A^{frac{r}{2}} B^p A^{frac{r}{2}})^{frac{r}{p+r}} $
for all $ p> 0$ and $ r> 0.$ ;


This article was printed from JIPAM
http://jipam.vu.edu.au

The URL for this article is:
http://jipam.vu.edu.au/article.php?sid=890