Totally accretive operators

Abstract

Let A A be a (possibly unbounded) linear operator on a Banach space. We show that, when A A generates a uniformly bounded strongly continuous semigroup { e − t A } t ≥ 0 {\left \{ {{e^{ - tA}}} \right \}_{t \geq 0}} , then A 2 {A^2} generates a bounded holomorphic semigroup (BHS) of angle θ \theta if and only if A A generates a BHS of angle θ / 2 + π / 4 \theta / 2 + \pi / 4 . We show that each power of A A generates a uniformly bounded strongly continuous semigroup if and only if A A generates a BHS of angle π / 2 \pi / 2 if and only if each power of A A generates a BHS of angle π / 2 \pi / 2 . If A A is a linear operator on a Hilbert space, then each power of A A generates a strongly continuous contraction semigroup if and only if A A is positive selfadjoint.