On the structure of a semigroup of operators with finite-dimensional ranges |
| |
Authors: | A. V. Pechkurov |
| |
Affiliation: | 1. Voronezh State University, Voronezh, Russia
|
| |
Abstract: | In the present paper, we describe the structure of a strongly continuous operator semigroup T(t) (where T: ?+ → End X and X is a complex Banach space) for which ImT(t) is a finite-dimensional space for all t > 0. It is proved that such a semigroup is always the direct sum of a zero semigroup and a semigroup acting in a finite-dimensional space. As examples of applications, we discuss differential equations containing linear relations, orbits of a special form, and the possibility of embedding an operator in a C 0-semigroup. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|