


Paper's Title:
Some criteria for Subspacehypercyclicity of C_{0}semigroups
Author(s):
Mansooreh Moosapoor
Department of Mathematics,
Farhangian University, Tehran,
Iran.
Email: m.mosapour@cfu.ac.ir
mosapor110@gmail.com
Abstract:
We research subspacehypercyclic C_{0}semigroups in this paper. We present various types of subspacehypercyclicity criteria for C_{0}semigroups. Some of them are stronger than the criteria introduced before. Also, we state that if a C_{0}semigroup (T_{t}}_{t≥ 0} satisfies in any of them, then (T_{t}⊕T_{t}}_{t≥ 0} is subspacehypercyclic.
Paper's Title:
On SubspaceSupercyclic Operators
Author(s):
Mansooreh Moosapoor
Assistant Professor,
Department of Mathematics,
Farhangian University, Tehran,
Iran.
Email: mosapor110@gmail.com
m.mosapour@cfu.ac.ir
Abstract:
In this paper, we prove that supercyclic operators are subspacesupercyclic and by this we give a positive answer to a question posed in ( L. Zhang, Z. H. Zhou, Notes about subspacesupercyclic operators, Ann. Funct. Anal., 6 (2015), pp. 6068). We give examples of subspacesupercyclic operators that are not subspacehypercyclic. We state that if T is an invertible supercyclic operator then T^{n} and T^{n} is subspacesupercyclic for any positive integer n. We give two subspacesupercyclicity criteria. Surprisingly, we show that subspacesupercyclic operators exist on finitedimensional spaces.
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