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arXiv · 1501.02534

Subspace-hypercyclic weighted shifts

Nareen Bamerni·Adem Kılıçman
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Abstract

Our aim in this paper is to obtain necessary and sufficient conditions for weighted shift operators on the Hilbert spaces $\ell^{2}(\mathbb Z)$ and $\ell^{2}(\mathbb N)$ to be subspace-transitive, consequently, we show that the Herrero question (D. A. Herrero. Limits of hypercyclic and supercyclic operators, J. Funct. Anal., 99 (1991)179-190) holds true even on a subspace of a Hilbert space, i.e. there exists an operator $T$ such that both $T$ and $T^*$ are subspace-hypercyclic operators for some subspaces. We display the conditions on the direct sum of two invertable bilateral forward weighted shift operators to be subspace-hypercyclic.

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Nareen Bamerni, Adem Kılıçman. 2015-01-12. Subspace-hypercyclic weighted shifts. https://arxiv.org/abs/1501.02534

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