A NOTE ON FREQUENT HYPERCYCLICITY OF OPERATORS THAT $$\lambda$$-COMMUTE WITH THE DIFFERENTIATION OPERATOR
A NOTE ON FREQUENT HYPERCYCLICITY OF OPERATORS THAT $$\lambda$$-COMMUTE WITH THE DIFFERENTIATION OPERATOR
Abstract A continuous linear operator on a Fréchet space $$\mathcal {X}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>X</mml:mi> </mml:math> is frequently hypercyclic if there exists a vector x such that for any nonempty open subset $$U\subset \mathcal {X}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>U</mml:mi> <mml:mo>⊂</mml:mo> <mml:mi>X</mml:mi> </mml:mrow> </mml:math> the set of $$n\in \mathbb {N}\cup \{0\}$$ <mml:math …