Subspace-recurrent C0-semigroups and their properties

Authors
Manooreh Moosapoor 1
Mohammad Shahriari 2
1 Farhangian University
2 University of Maragheh
Abstract
In this paper, we prove that these C0-semigroups exist on every infinite-dimensional Banach space. It is shown that C0-semigroups can be constructed on finite-dimensional Banach spaces and with respect to finite-dimensional subspaces. We define subspace-recurrent vectors for C0-semigroups and state that any C0-semigroup that has a dense set of subspace-recurrent vectors is subspace-recurrent. Moreover, we prove that any recurrent C0-semigroup is subspace-recurrent. Also, some sufficient conditions for subspace-recurrency are proved that are based on dense sets and open sets.
Keywords
subspace-recurrent C0-semigroup
recurrent C0-semigroup
subspace-recurrent vector
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