HYPERCYCLICITY OF OPERATORS THAT $$\lambda$$-COMMUTE WITH THE HARDY BACKWARD SHIFT
Copyright policy )HYPERCYCLICITY OF OPERATORS THAT $$\lambda$$-COMMUTE WITH THE HARDY BACKWARD SHIFT
AbstractAn operator T acting on a separable complex Banach space $$\mathcal {B}$$ B is said to be hypercyclic if there exists $$f\in \mathcal {B}$$ f ∈ B such that the orbit $$\{T^n f:\ n\in \mathbb {N}\}$$ { T n f : n ∈ N } is dense in $$\mathcal {B}$$ 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 $$\lambda$$ λ -commute with the Hardy backward shift B, that is, $$BX=\lambda XB$$ B X = λ X B .
- Chouaib Doukkali University Morocco
- University of Cádiz Spain
Artificial intelligence, Spaces of differentiable or holomorphic functions on infinite-dimensional spaces, Classification and Properties of C*-Algebras, extended eigenoperators, 47A16, 37B20, FOS: Mathematics, space of entire functions, Shift operator, Complex Analysis and Operator Theory, Operator Theory, Mathematical Physics, Holomorphic maps in nonlinear functional analysis, shift operator, Applied Mathematics, Geometric Function Theory and Complex Analysis, Cyclic vectors, hypercyclic and chaotic operators, Hypercyclic operators, hypercyclic operators, Computer science, Functional Analysis (math.FA), Mathematics - Functional Analysis, Algorithm, Space of entire functions, Hypercyclic Operators, Physical Sciences, Extended eigenoperators, Notions of recurrence and recurrent behavior in topological dynamical systems, Geometry and Topology, Mathematics
Artificial intelligence, Spaces of differentiable or holomorphic functions on infinite-dimensional spaces, Classification and Properties of C*-Algebras, extended eigenoperators, 47A16, 37B20, FOS: Mathematics, space of entire functions, Shift operator, Complex Analysis and Operator Theory, Operator Theory, Mathematical Physics, Holomorphic maps in nonlinear functional analysis, shift operator, Applied Mathematics, Geometric Function Theory and Complex Analysis, Cyclic vectors, hypercyclic and chaotic operators, Hypercyclic operators, hypercyclic operators, Computer science, Functional Analysis (math.FA), Mathematics - Functional Analysis, Algorithm, Space of entire functions, Hypercyclic Operators, Physical Sciences, Extended eigenoperators, Notions of recurrence and recurrent behavior in topological dynamical systems, Geometry and Topology, Mathematics
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