ON SUBSPACE-HYPERCYCLIC AND SUPERCYCLIC SEMIGROUP

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IJPAM: Volume 116, No. 4 (2017)

Title

ON SUBSPACE-HYPERCYCLIC
AND SUPERCYCLIC SEMIGROUP

Authors

A. Tajmouati

, M. El Berrag

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

is called subspace-hypercyclic (resp. subspace-supercyclic) for a subspace

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

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

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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