[HTML][HTML] HYPERCYCLICITY OF OPERATORS THAT -COMMUTE WITH THE HARDY BACKWARD SHIFT
Journal of Mathematical Sciences, 2024•Springer
An operator T acting on a separable complex Banach space B is said to be hypercyclic if
there exists f∈ B such that the orbit {T nf: n∈ N} is dense in B. Godefroy and Shapiro (J.
Funct. Anal., 98 (2): 229–269, 1991) characterized those elements, which are hypercyclic, in
the commutant of the Hardy backward shift. In this paper, we study some dynamical
properties of operators X that λ-commute with the Hardy backward shift B, that is, BX= λ XB.
there exists f∈ B such that the orbit {T nf: n∈ N} is dense in B. Godefroy and Shapiro (J.
Funct. Anal., 98 (2): 229–269, 1991) characterized those elements, which are hypercyclic, in
the commutant of the Hardy backward shift. In this paper, we study some dynamical
properties of operators X that λ-commute with the Hardy backward shift B, that is, BX= λ XB.
Abstract
An operator T acting on a separable complex Banach space is said to be hypercyclic if there exists such that the orbit is dense in . Godefroy and Shapiro (J. Funct. Anal., 98(2):229–269, 1991) characterized those elements, which are hypercyclic, in the commutant of the Hardy backward shift. In this paper, we study some dynamical properties of operators X that -commute with the Hardy backward shift B, that is, .
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