IJPAM: Volume 88, No. 3 (2013)

ON POINT SPECTRUM OF
SUBSPACE-HYPERCYCLIC OPERATORS

Mansooreh Moosapoor
Farhangian University
Postcode 4166616711, Rasht, IRAN


Abstract. It is well known that if $T$ is a hypercyclic operator, then $ \sigma_{p} (T^{*}) = \phi$. We prove in this paper that this is not true for subspace-hypercyclic operators. We show that if $T$ is subspace-hypercyclic, then $\sigma_{p}(T^{*})$ may be empty or not. Moreover we show that for every scalar $\lambda$ with $\vert\lambda\vert>1$, there exists a subspace-hypercyclic operator $T$ such that $\vert\vert T\vert\vert=\vert\lambda\vert $ and $ \sigma_{p} (T^{*}) \neq \phi$.

Received: July 10, 2013

AMS Subject Classification: 47A16, 47B37, 37B99

Key Words and Phrases: subspace-hypercyclic operators, point spectrum

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DOI: 10.12732/ijpam.v88i3.8 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: 2013
Volume: 88
Issue: 3