Supercyclic vectors of operators on normed linear spaces

2022/06/03 by Mohammad Ansari, Ansari, Mohammad
Mathematics · #46B20 #47A16 #Approximation Theory and Sequence Spaces #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2206.01508

openalex publication_date 2022/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an affirmative answer to a question asked by Faghih-Ahmadi and Hedayatian regarding supercyclic vectors. We show that if \mathcal X is an infinite-dimensional normed linear space and T is a supercyclic operator on \mathcal X, then for any supercyclic vector x for T, there exists a strictly increasing sequence (n_k)_k of positive integers such that the closed linear span of the set \T^n_kx: k≥ 1\ is not the whole \mathcal X.

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