Weighted Composition Operators and Supercyclicity Criterion

Abstract

We consider an equivalent condition to the property of Supercyclicity Criterion, and then we investigate this property for the adjoint of weighted composition operators acting on Hilbert spaces of analytic functions.

Disk-cyclic and Codisk-cyclic tuples of the adjoint weighted composition operators on Hilbert spaces

“…The Riesz representation theorem states that e λ ( f ) = f , k λ for some k λ ∈ H, the reproducing kernel of H. The collection of all holomorphic functions (or self-maps) in D is denoted as H(D) (or S(D)). Recently, hypercyclic and supercyclic operators have received considerable attention, especially since they arise in familiar classes of operators, such as weighted shifts [5,6,12,13,14,20], composition operators [15], weighted composition operators [4,11,16,19,21,22,23]. For motivation, examples and background about linear dynamics, we refer the readers to the excellent books [2] by Bayart and Matheron, [7] by Grosse-Erdmann and Peris Manguillot.…”

Dynamics of Parabolic Weighted Composition Operators

“…For simplicity, we call a weighted composition operator C ϕ,ψ , a parabolic weighted composition operator whenever the compositional symbol ψ is parabolic. For some sources see [1][2][3][4][5][6][7][8][9].…”

Tuple of Operators and Epsilon Supercyclicity

“…A tuple of operators is ǫ-supercyclic if it admits an ǫ-supercyclic vector. For some sources on these topics see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”