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Spectra of generalized stochastic adding machines

Volume 241 / 2018

Ali Messaoudi, Glauco Valle Fundamenta Mathematicae 241 (2018), 17-43 MSC: Primary 37A30, 37F50; Secondary 47A10. DOI: 10.4064/fm361-2-2017 Published online: 11 August 2017

Abstract

We define stochastic adding machines based on Cantor systems of numeration. We show that the spectra associated to these stochastic adding machines are fibered Julia sets, and we also compute various parts of the spectra of their transition operators in different Banach spaces, like $c_0$, $c$ and $l^{\alpha }$, $1 \leq \alpha \leq \infty $.

Authors

  • Ali MessaoudiDepartamento de Matemática do Instituto de Biociências Letras e Ciências Exatas
    UNESP
    Rua Cristóvão Colombo, 2265
    Jardim Nazareth
    15054-000–São José do Rio Preto, SP, Brazil
    e-mail
    e-mail
  • Glauco ValleInstituto de Matemática
    Universidade Federal do Rio de Janeiro
    Caixa Postal 68530
    CEP 21945-970, Rio de Janeiro, Brazil
    e-mail

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