36 research outputs found

    Strongly nn-supercyclic operators

    Get PDF
    In this paper, we are interested in the properties of a new class of operators, recently introduced by Shkarin, called strongly nn-supercyclic operators. This notion is stronger than nn-supercyclicity. We prove that such operators have interesting spectral properties and give examples and counter-examples answering some natural questions asked by Shkarin

    Operators commuting with the Volterra operator are not weakly supercyclic

    Full text link
    We prove that any bounded linear operator on Lp[0,1]L_p[0,1] for 1p<1\leq p<\infty, commuting with the Volterra operator VV, is not weakly supercyclic, which answers affirmatively a question raised by L\'eon-Saavedra and Piqueras-Lerena. It is achieved by providing an algebraic flavored condition on an operator which prevents it from being weakly supercyclic and is satisfied for any operator commuting with VV.Comment: Submitted to LM

    Simultaneous universality

    Get PDF
    In this paper, the notion of simultaneous universality is introduced, concerning operators having orbits that simultaneously approximate any given vector. This notion is related to the well known concepts of universality and disjoint universality. Several criteria are provided, and several applications to specific operators or sequences of operators are performed, mainly in the setting of sequence spaces or spaces of holomorphic functions.Plan Andaluz de Investigación (Junta de Andalucía)Ministerio de Economía y CompetitividadDeutsche Forschungsgemeinschaf

    Common hypercyclic vectors for families of operators

    Get PDF
    We provide a criterion for the existence of a residual set of common hypercyclic vectors for an uncountable family of hypercyclic operators which is based on a previous one given by Costakis and Sambarino. As an application, we get common hypercyclic vectors for a particular family of hypercyclic scalar multiples of the adjoint of a multiplier in the Hardy space, generalizing recent results by Abakumov and Gordon and also Bayart. The criterion is applied to other specific families of operators

    Hypercyclic subspaces in Fréchet spaces

    Get PDF
    In this note, we show that every infinite-dimensional separable Fr´echet space admitting a continuous norm supports an operator for which there is an infinite-dimensional closed subspace consisting, except for zero, of hypercyclic vectors. The family of such operators is even dense in the space of bounded operators when endowed with the strong operator topology. This completes earlier work of several authors.Plan Andaluz de Investigación (Junta de Andalucía)Dirección General de Enseñanza Superior (DGES). Españ
    corecore