Home About Upload Latest Additions Statistics Contact
UT Proceedings
UT Student Theses
Dutch Academic Output Dutch Dissertations EU Publications (OpenAIRE)
Printversion
Advanced search

Is $A^{-1}$ an infinitesimal generator?

Share/Save/Bookmark

Zwart, H.J. (2007) Is $A^{-1}$ an infinitesimal generator? Banach center publications, 75 . pp. 303-313. ISSN 0137-6934

[img]PDF
Restricted to UT campus only: Request a copy
135Kb
Abstract:In this paper we study the question whether $A^{-1}$ is the infinitesimal generator of a bounded $C_0$-semigroup if $A$ generates a bounded $C_0$-semigroup. If the semigroup generated by $A$ is analytic and sectorially bounded, then the same holds for the semigroup generated by $A^{-1}$. However, we construct a contraction semigroup with growth bound minus infinity for which $A^{-1}$ does not generate a bounded semigroup. Using this example we construct an infinitesimal generator of a bounded semigroup for which its inverse does not generate a semigroup. Hence we show that the question posed by deLaubenfels in 1988 must be answered negatively. All these examples are on Banach spaces. On a Hilbert space the question whether the inverse of a generator of a bounded semigroup also generates a bounded semigroup still remains open.
Item Type:Article
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
Research Group:
Link to this item:http://purl.utwente.nl/publications/61749
Official URL:http://journals.impan.gov.pl/bc/index.html
Export this item as:BibTeX
EndNote
HTML Citation
Reference Manager

 

Repository Staff Only: item control page

Metis ID: 241681