Convex-cyclic and super convex-cyclic weighted shifts

Convex-cyclic operators are considered by H. Rezaei \cite{R1}. However, there is a general lack of theoretical understanding of super convex-cyclic operators. In this paper, we analyze super convex-cyclic operators. In particular, Super Convex-cyclicity Criterion is described. Additionally, we characterize convex-cyclicity of (invertible) bilateral weighted shifts in terms of their weight sequences, which in turn correct \cite[H. Rezaei (2013) Theorem 4.2 ]{R1}. Meanwhile, we give super convex-cyclicity of (invertible) weighted shifts in the bilateral case.