On the Recurrent
C
0
-Semigroups, Their Existence, and Some Criteria
Keyword(s):
In this paper, recurrent C 0 -semigroups are introduced and investigated. It is proved that, despite hypercyclic C 0 -semigroups, recurrent C 0 -semigroups can be found on finite-dimensional Banach spaces. Some criteria are stated for recurrence, which is based on open sets, neighborhoods of zero, and special eigenvectors. It is established that having a dense set of recurrent vectors is a sufficient and necessary condition for a C 0 -semigroup to be recurrent. Moreover, the direct sum of recurrent C 0 -semigroups is investigated.
Keyword(s):
2013 ◽
Vol 89
(2)
◽
pp. 234-242
◽
2018 ◽
Vol 16
(06)
◽
pp. 1850053
◽