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## Banach Center Publications

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## 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.

#### Authors

• Alexander GomilkoFaculty of Mathematics and Computer Science
Nicolas Copernicus University
Chopina str. 12/18
87-100 Toruń, Poland
e-mail

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