On the topology induced by the adjoint of a semigroup of operators |
| |
Authors: | J M A M van Neerven |
| |
Institution: | (1) Centre for Mathematics and Computer Science, P.O. Box 4079, 1009 AB Amsterdam, The Netherlands |
| |
Abstract: | The adjoint of aC
0-semigroup on a Banach spaceX induces a locally convex σ(X,X
ℴ)-topology inX, which is weaker than the weak topology ofX. In this paper we study the relation between these two topologies. Among other things a class of subsets ofX is given on which they coincide. As an application, an Eberlein-Shmulyan type theorem is proved for the σ(X,X
ℴ)-topology and it is shown that the uniform limit of σ(X,X
ℴ)-compact operators is σ(X,X
ℴ)-compact. Finally our results are applied to the problem when the Favard class of a semigroup equals the domain of the infinitesimal
generator. |
| |
Keywords: | 47D05 |
本文献已被 SpringerLink 等数据库收录! |
|