Boulabiar, Karim A Hölder-type inequality for positive functionals on \(\Phi\)-algebras. (English) Zbl 1022.06008 JIPAM, J. Inequal. Pure Appl. Math. 3, No. 5, Paper No. 74, 7 p. (2002). Summary: 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 \(T(|fg|) \leq(T(|f|^p))^{1/p} (T(|g|^q))^{1/q}\) holds for all \(f,g\in A\). MSC: 06F25 Ordered rings, algebras, modules 47B65 Positive linear operators and order-bounded operators Keywords:Hölder inequality; positive linear functional; \(f\)-algebra; uniformly complete \(\Phi\)-algebra; constructive proof PDFBibTeX XMLCite \textit{K. Boulabiar}, JIPAM, J. Inequal. Pure Appl. Math. 3, No. 5, Paper No. 74, 7 p. (2002; Zbl 1022.06008) Full Text: EuDML