IJPAM: Volume 116, No. 4 (2017)

Title

ON SUBSPACE-HYPERCYCLIC
AND SUPERCYCLIC SEMIGROUP

Authors

A. Tajmouati$^1$, M. El Berrag$^2$
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 a infinite-dimensional separable complex Banach space $X,$ is called subspace-hypercyclic (resp. subspace-supercyclic) for a subspace $M,$ if $Orb(\mathcal{T},x)\bigcap M$ ( resp. $\mathbb{C}Orb(\mathcal{T},x)\bigcap M = \{\lambda T_{t}x:
\lambda\in \mathbb{C}, t\geq0 \}\bigcap M$) is dense in $M$ for a vector $x\in M$. In this paper we provide a Subspace-hypercyclicity Criterion and we show if $\mathcal{T}=(T_{t})_{t\geq0}$ and $\mathcal{S}=(S_{t})_{t\geq0}$ are $C_{0}$-semigroups and $M_{1},
M_{2}$ are nonzero closed subspaces of $X$ and $(T_{t}\oplus
S_{t})_{t\geq0}$ is $(M_{1}\oplus M_{2})$-hypercyclic $C_{0}$-semigroups, then $\mathcal{T}$ and $\mathcal{S}$ are $M_{1}$-hypercyclic and $M_{2}$-hypercyclic $C_{0}$-semigroups , respectively. At the same time, we also characterize other properties of subspace-hypercyclic (resp. subspace-supercyclic) $C_{0}$-semigroup.

History

Received: 2016-12-13
Revised: 2017-06-29
Published: November 7, 2017

AMS Classification, Key Words

AMS Subject Classification: 47A16, 46B37
Key Words and Phrases: $C_{0}$-semigroup, subspace-supercyclic space, subspace-hypercyclic space, subspace-hypercyclicity criterion, $C_{0}$-semigroup

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How to Cite?

DOI: 10.12732/ijpam.v116i4.2 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 116
Issue: 4
Pages: 819 - 827


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