Two remarks on the set of recurrent vectors

[en] We solve in the negative two open problems, related to the linear and topological structure of the set of recurrent vectors, asked by Sophie Grivaux, Alfred Peris and the first author of this paper. Firstly, we show that there exist recurrent operators whose set of recurrent vectors is not dense lineable; and secondly, we construct operators which are reiteratively recurrent and cyclic, but whose set of reiteratively recurrent vectors is meager.

Disciplines :

Mathematics

Author, co-author :

López-Martínez, Antoni; Universitat Politècnica de València, Institut Universitari de Matemàtica Pura i Aplicada, València, Spain

Menet, Quentin ; Université de Mons - UMONS > Faculté des Sciences > Service d'Analyse fonctionnelle

Language :

English

Title :

Two remarks on the set of recurrent vectors

Publication date :

2025

Journal title :

Journal of Mathematical Analysis and Applications

ISSN :

0022-247X

eISSN :

1096-0813

Publisher :

Academic Press Inc.

Volume :

541

Issue :

Pages :

128686

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://api.elsevier.com/content/article/PII:S0022247X24006085?httpAccept=text/xml

Research unit :

S844 - Probabilité et statistique

Research institute :

R150 - Institut de Recherche sur les Systèmes Complexes

Funding text :

The first author was supported by the Spanish Ministerio de Ciencia, Innovaci\u00F3n y Universidades, grant FPU2019/04094; by MCIN/AEI/10.13039/501100011033, Projects PID2019-105011GB-I00 and PID2022-139449NB-I00; and by the \u201CFundaci\u00F3 Ferran Sunyer i Balaguer\u201D. The second author is a Research Associate of the Fonds de la Recherche Scientifique - FNRS.

Available on ORBi UMONS :

since 06 January 2025

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Bibliography

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