IJPAM: Volume 109, No. 4 (2016)


A. Tajmouati$^1$, M. El Berrag$^2$
$^{1,2}$Faculty of Sciences
Sidi Mohamed Ben Abdellah University
Dhar El Mahraz Fez, MOROCCO

Abstract. A $C_{0}$-semigroup $\mathcal{T}=(T_{t})_{t\geq0}$ on an infinite-dimensional separable complex Banach space $X$ is called subspace-hypercyclic for a subspace $M,$ if $Orb(\mathcal{T},x)\bigcap M$ is dense in $M$ for a vector $x\in M$. In this paper, we localize the notion of M-extended semigroup(resp. M-extended semigroup mixing) limit set of $x$ under $\mathcal{T}$ and We give sufficient conditions of being $M$-hypercyclic for this semigroup. Then by this result, we prove that $(T_{t}^{-1})_{t\geq0}$ is a $M$-hypercyclic. This result is an answer of the question of B. F. Madore and R. A. Martnez-Avendano for $C_{0}$-semigroup.

Received: June 12, 2016

Revised: September 3, 2016

Published: October 9, 2016

AMS Subject Classification: 47C03, 47A10, 47A11

Key Words and Phrases: $C_{0}$-semigroup, subspace-hypercyclic, subspace-topologically transitive, $J-$class semigroup, $J^{mix}-$class semigroup
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DOI: 10.12732/ijpam.v109i4.9 How to cite this paper?

International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 109
Issue: 4
Pages: 861 - 868

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