Year: 2025
Type: article
Abstract: This paper concerns the spectral structure of hypercyclic and supercyclic operators defined on Banach spaces, or defined on Hilbert spaces. We also consider the spectral properties of operators in Hilbert spaces that commute with a hypercyclic operator. A result of Herrero and Kitai (Proc Am Math Soc 116(3):873–875, 1992) is extended to Drazin invertible operators. In particular, a Drazin invertible operator is hypercyclic if and only if is invertible. An analogous result holds for supercyclic operators T in the case were the dual $$T^*$$ T ∗ has empty point spectrum.
Source: Advances in Operator Theory
Authors: Pietro Aiena, Fabio Burderi, Salvatore Triolo
Institution: University of Palermo
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Award: G5759732000
OpenAlex ID: W4409965599