Complex Analysis and Operator Theory

, Volume 11, Issue 3, pp 491–505 | Cite as

On Chaoticity of the Sum of Chaotic Shifts with Their Adjoints in Hilbert Space and Applications to Some Weighted Shifts Acting on Some Fock–Bargmann Spaces

Article

Abstract

The aim in this paper is to give sufficient conditions for an operator of the form \(\mathbb {T} + \mathbb {T}^{*}\) to be chaotic (in the sense of Devaney). Here \(\mathbb {T}\) is assumed to be a weighted chaotic shift operator on a Hilbert space and \(\mathbb {T}^{*}\) is its adjoint. Sufficient conditions on the weight sequence are given and then applied to some particular bakward shift unbounded operators realized as differential operators acting on some Fock–Bargmann spaces.

Keywords

Chaotic operators Weighted shift unbounded operators  Analytic functions Fock–Bargmann spaces Gelfond–Leontiev operators Spectral analysis 

Mathematics Subject Classification

46C 47B 47F 32K 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Equipe d’Analyse spectrale, Faculté des Sciences et TechniquesUniversité de CortéCortéFrance
  2. 2.Ecole Saint-GenevièveAcadémie de VersaillesVersaillesFrance
  3. 3.Le PradorMarseilleFrance

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