A Holder-type inequality for Positive Functionals on $\Phi$-Algebras

Volume 3, Issue 5, 2002

Article 74

A HÖLDER-TYPE INEQUALITY FOR POSITIVE FUNCTIONALS ON F-ALGEBRAS

DÉPARTEMENT DE MATHÉMATIQUES,
FACULTÉ DES SCIENCES DE BIZERTE,
UNIVERSITÉ DU 7 NOVEMBRE À CARTHAGE,
7021-ZARZOUNA, TUNISIA.
E-Mail: karim.boulabiar@ipest.rnu.tn

Received 4 February, 2002; Accepted 31 August, 2002.
Communicated by: S.S. Dragomir

ABSTRACT. The main purpose of this paper is to establish with a constructive proof the following Hölder-type inequality: let

be a uniformly complete $\Phi$ -algebra,

be a positive linear functional, and

be rational numbers such that $p^{-1}+q^{-1}=1$ . Then the inequality

$\displaystyle T\left( \left\vert fg\right\vert \right) \leq\left( T\left( \left... ...\right) ^{1/p}\left( T\left( \left\vert g\right\vert ^{q}\right) \right) ^{1/q}$

holds for all $f,g\in A.$

Key words:
Hölder inequality, Positive linear functional, f-algebra, Uniformly complete f-algebra.

2000 Mathematics Subject Classification:
06F25, 47B65

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