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Inequalities for $J-$Contractions Involving the $ \alpha-$Power Mean  
 
  Authors: G. Soares,  
  Keywords: $J-$selfadjoint matrix, Furuta inequality, $J-$chaotic order, $lpha-$power mean.  
  Date Received: 22/06/2009  
  Date Accepted: 14/10/2009  
  Subject Codes:

47B50, 47A63, 15A45.

  
  Editors: Sever S. Dragomir,  
 
  Abstract:

A selfadjoint involutive matrix $J$ endows $ mathbb{C}^n$ with an indefinite inner product $[ cdot, cdot]$ given by $[x,y]:= langle J x, y rangle$, $x,y in mathbb{C}^n.$ We present some inequalities of indefinite type involving the $ alpha-$power mean and the chaotic order. These results are in the vein of those obtained by E. Kamei [6, 7]. ;


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