2024/12/26 by Song-Ung Ri, Ri, SongUng, Hyonhui Ju +3
Mathematics · #47A16 #47B37 #Advanced Topics in Algebra #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory in Mathematical Physics #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2412.19115
openalex publication_date 2024/12/26 · openalex created_date 2024/12/31 · openalex updated_date 2026/07/28
We first give a note on disjoint hypercyclicity for invertible bilateral pseudo-shifts on ℓp(ℤ), 1≤ p <∞. It is already known that if a tuple of bilateral weighted shifts on ℓp(ℤ), 1≤ p <∞, is disjoint hypercyclic, then non of the weighted shifts is invertible. We show that as for pseudo-shifts which is a generalization of weighted shifts, this fact is not true. We give an example of invertible bilateral pseudo-shifts on ℓp(ℤ), 1≤ p <∞, which are disjoint hypercyclic and whose inverses are also disjoint hypercyclic. Next we partially answer to the open problem posed by Martin, Menet and Puig (2022)\citeMMP22 concerned with disjoint reiteratively hypercyclic, that is, we show that as for the operators on a reflexive Banach space, reiteratively hypercyclic ones are disjoint hypercyclic if and only if they are disjoint reiteratively hypercyclic.