Subspace-hypercyclic weighted shifts

2015/01/12 by Nareen Bamerni, Adem Kılıçman, Bamerni, Nareen +1
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1501.02534

arxiv created 2015/01/12 · arxiv updated 2015/01/13

Abstract

Our aim in this paper is to obtain necessary and sufficient conditions for weighted shift operators on the Hilbert spaces ℓ²(\mathbb Z) and ℓ²(\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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