Title:	The double transpose of the Ruelle operator
Authors:	Cioletti, Leandro Martins Enter, A. van Ruviaro, Ricardo
metadata.dc.identifier.orcid:	https://orcid.org/0000-0002-8131-2043
metadata.dc.contributor.affiliation:	Universidade de Brasília Johann Bernoulli Instituut, Rijksuniversiteit Groningen, Nijenborgh 9, 9747 AG Groningen, The Netherlands Universidade de Brasília
Assunto::	Operador de Ruelle Teoria Ergódica
Issue Date:	3-Jan-2023
Publisher:	Springer
Citation:	CIOLETTI, L.; ENTER, A. van; RUVIARO, R. The double transpose of the Ruelle operator. Monatshefte für Mathematik, 2023. DOI: https://doi.org/10.1007/s00605-022-01818-7.
Abstract:	In this paper we study the double transpose of the L1(X, B(X), ν)-extensions of the Ruelle transfer operator L f associated to a general real continuous potential f ∈ C(X), where X = EN, the alphabet E is any compact metric space and ν is a maximal eigenmeasure. For this operator, denoted by L∗∗ f , we prove the existence of some non negative eigenfunction, in the Banach lattice sense, associated to ρ(L f ), the spectral radius of the Ruelle operator acting on C(X). As an application, we obtain a sufficient condition ensuring that the extension of the Ruelle operator to L1(X, B(X), ν) has an eigenfunction associated to ρ(L f ). These eigenfunctions agree with the usual maximal eigenfunctions, when the potential f belongs to the Hölder,Walters or Bowen class. We also construct solutions to the classical and generalized variational problem, using the eigenvector constructed here.
metadata.dc.description.unidade:	Instituto de Ciências Exatas (IE) Departamento de Matemática (IE MAT)
DOI:	https://doi.org/10.1007/s00605-022-01818-7
metadata.dc.relation.publisherversion:	https://link.springer.com/article/10.1007/s00605-022-01818-7
Appears in Collections:	Artigos publicados em periódicos e afins

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