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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.

Majorization of C 0 -semigroups in ordered Banach spaces

Gerd Herzog, Peer Christian Kunstmann (2006)

Commentationes Mathematicae Universitatis Carolinae

We give criteria for domination of strongly continuous semigroups in ordered Banach spaces that are not necessarily lattices, and thus obtain generalizations of certain results known in the lattice case. We give applications to semigroups generated by differential operators in function spaces which are not lattices.

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