Generators of positiveC0-semigroups
Shizuo Miyajima, Noboru Okazawa · Pacific Journal of Mathematics · 1986
By the use of abstract Kato's inequality for generators of positive C 0 -semigroups, it is shown that a differential operator with smooth coefficients (with natural domain) is of order at most 2 and (degenerate) elliptic provided it generates a positive C 0 -semigroup on L p (R n ) (1 0 be a C 0 -semigroup of linear operators on a Banach lattice E with generator A. Then {T t } t > 0 is said to be positive if T t is positive for any t > 0, namely T t u > 0 whenever u > 0. The resolvent (λ -A)' 1 of A is denoted by R(λ, A).Then the equalities T t = s-]im[(n/t)R((n/t),A)V(t > 0), 161 162 SHIZUO MIYAJIMA AND NOBORU OKAZAWA