M. Meyries

A solution to the inverse generator problem and related questions

We give a negative solution to the inverse generator problem on Hilbert spaces. More precisely, we construct a bounded operator $A$ with dense range on a Hilbert space $H$ that generates a bounded, strongly stable $C_0$-semigroup, while $A^{-1}$ does not generate a $C_0$-semigroup. We also construct an exponentially st...