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A Hölder-type Inequality for Positive Functionals on $f$-Algebras  
 
  Authors: Karim Boulabiar,  
  Keywords: Hölder inequality, Positive linear functional, $f$-algebra, Uniformly complete $f$-algebra.  
  Date Received: 04/02/02  
  Date Accepted: 31/09/02  
  Subject Codes:

06F25,47B65

  
  Editors: Sever S. Dragomir,  
 
  Abstract:

The main purpose of this paper is to establish with a constructive proof the following Hölder-type inequality: let $ A$ be a uniformly complete $ Phi $-algebra, $ T$ be a positive linear functional, and $ p,q$ be rational numbers such that $ p^{-1}+q^{-1}=1$. Then the inequality

$displaystyle Tleft( leftvert fgrightvert right) leqleft( Tlef ( left... ...right) ^{1/p}left( Tleft( leftvert grightvert ^{q}right) right) ^{1/q}$    
holds for all $ f,gin A.$;


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