Abstract

This chapter focuses on the generators of positive C o -semigroups. It presents an exposition of some earlier results in a slightly improved form. The problem to be treated is concerned with the generators of positive C o -semigroups on Banach lattices. Abstract Kato's inequality for the generators of positive semigroups and Kato's inequality for formal differential operators are presented in the chapter. The generators of such semigroups satisfy weak abstract Kato's inequality, and if a differential operator generates a positive C o- semigroup on L p (Ω) then it is an (possibly degenerate) elliptic second order differential operator. An improvement of a result of Baoswan Wong–Dzung is also presented in the chapter.

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