Paper's Title:

Some criteria for Subspace-hypercyclicity of C₀-semigroups

Author(s):

Mansooreh Moosapoor

Department of Mathematics,
Farhangian University, Tehran,
Iran.
E-mail: m.mosapour@cfu.ac.ir
mosapor110@gmail.com
 

Abstract:

We research subspace-hypercyclic C₀-semigroups in this paper. We present various types of subspace-hypercyclicity criteria for C₀-semigroups. Some of them are stronger than the criteria introduced before. Also, we state that if a C₀-semigroup (T_t}_{t≥ 0} satisfies in any of them, then (T_t⊕T_t}_{t≥ 0} is subspace-hypercyclic.

Paper's Title:

On Subspace-Supercyclic Operators

Author(s):

Mansooreh Moosapoor

Assistant Professor,
Department of Mathematics,
Farhangian University, Tehran,
Iran.
E-mail: mosapor110@gmail.com m.mosapour@cfu.ac.ir

Abstract:

In this paper, we prove that supercyclic operators are subspace-supercyclic and by this we give a positive answer to a question posed in ( L. Zhang, Z. H. Zhou, Notes about subspace-supercyclic operators, Ann. Funct. Anal., 6 (2015), pp. 60--68). We give examples of subspace-supercyclic operators that are not subspace-hypercyclic. We state that if T is an invertible supercyclic operator then Tⁿ and T^-n is subspace-supercyclic for any positive integer n. We give two subspace-supercyclicity criteria. Surprisingly, we show that subspace-supercyclic operators exist on finite-dimensional spaces.

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