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Inequalities between the sum of powers and the exponential of sum of positive and commuting selfadjoint operators

Berrabah Bendoukha, Hafida Bendahmane (2011)

Archivum Mathematicum

Let ( ) be the set of all bounded linear operators acting in Hilbert space and + ( ) the set of all positive selfadjoint elements of ( ) . The aim of this paper is to prove that for every finite sequence ( A i ) i = 1 n of selfadjoint, commuting elements of + ( ) and every natural number p 1 , the inequality e p p p i = 1 n A i p exp i = 1 n A i , holds.

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