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  Volume 8, Issue 3, Article 62
 
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.$

         
       
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