A Hölder-type Inequality for Positive Functionals on Φ-algebras
نویسندگان
چکیده
The main purpose of this paper is to establish with a constructive proof the following Hölder-type inequality: let A be a uniformly complete Φ-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|) ≤ (T (|f |)) (T (|g|)) holds for all f, g ∈ A.
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