Inverses of semigroup generators: a survey and remarks
Volume 112 / 2017
Banach Center Publications 112 (2017), 107-142
MSC: 47D06.
DOI: 10.4064/bc112-0-7
Abstract
Let $X$ be a Banach space, and let $(e^{tA})_{t \ge 0}$ be a bounded $C_0$-semigroup on $X$, with generator $A$. Suppose that $A^{-1}$ exists as a (closed) densely defined operator. In 1988 deLaubenfels asked whether $A^{-1}$ also generates a $C_0$-semigroup. The problem is still open in the setting of Hilbert spaces. In this survey we will discuss partial advances obtained so far and mention also related results.
