HEREDITARILY HYPERCYCLICITY AND SUPERCYCLICITY OF WEIGHTED SHIFTS
HEREDITARILY HYPERCYCLICITY AND SUPERCYCLICITY OF WEIGHTED SHIFTS
In this paper we first characterize the hereditarily hypercyclicity of the unilateral (or bilateral) weighted shifts on the spaces <TEX>$L^2(\mathbb{N},\mathcal{K})$</TEX> (or <TEX>$L^2(\mathbb{Z},\mathcal{K})$</TEX>) with weight sequence {<TEX>$A_n$</TEX>} of positive invertible diagonal operators on a separable complex Hilbert space <TEX>$\mathcal{K}$</TEX>. Then we give the necessary and sufficient conditions for the supercyclicity of …