Hypercyclicity of special operators on Hilbert function spaces

Cyclicity of the adjoint of weighted composition operators on the hilbert space of analytic functions

“…In [14] the authors claimed "as a theorem" that the adjoint of a weighted composition operator M w C ϕ is hypercyclic on H if ϕ is an automorphism, the composition operator C ϕ is bounded and w is a non-constant multiplier such that the sets {λ ∈ D : sup If a 1 = a + 1, a n+1 = (2a + 1)a n − a for n 1, then using induction we see that a + 1 a n ; moreover, ϕ n (z) = z + α n 1 + α n z , where α n = a n − 1 a n and w • ϕ n (z) = ((a n − 1)z + a n ) √ 2a + 1 (2aa n + a n − a − 1)z + 2aa n + a n − a .…”

“…Now assume that G F is not necessarily linearly independent. In this case, we use the same method as the one used by Godefroy and Shapiro in Theorem 4.5 of [8] or [14]. Consider a countable dense subset F 1 = {λ n : n > 0} of F , and using induction choose a sequence {z n } n as follows.…”

“…The hypercyclicity of the adjoint of a weighted composition operator on a Hilbert space of analytic functions is investigated in [14] and [15]. In this paper, we first give counterexamples to the main result of [14] and then establish sufficient conditions for hypercyclicity, supercyclicity and cyclicity of the adjoint of a weighted composition operator.…”

“…In this paper, we first give counterexamples to the main result of [14] and then establish sufficient conditions for hypercyclicity, supercyclicity and cyclicity of the adjoint of a weighted composition operator.…”

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].…”