2024/07/16 by Rodrigo Cardeccia, Cardeccia, Rodrigo, Santiago Muro +1
Mathematics · #37A46 #37B20 #47A16 #47A35 #47B37 #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.2407.11799
openalex publication_date 2024/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study frequently recurrent unilateral and bilateral backward shift operators on Fréchet sequence spaces. We prove that if a backward shift admits a non-zero frequently recurrent vector, then it supports a dense set of such vectors, so that the operator is frequently recurrent. As a consequence, we provide two different characterizations for frequently recurrent backward shift operators and we show dense lineability of the set of the set of frequently recurrent vectors.