A bounded linear operator T on a complex Banach space $\mathcal{X}$ is superconvex-cyclic, if for some vector x in the space, $\mathbb{C}.co(orb(T,x))$ is dense. Here, co(orb(T, x)) means the convex hull of $\{T^{n}x:n\ge 0\}$. In this paper, we give necessary conditions for the superconvex-cyclicity of an operator in terms of the point spectrum of its adjoint. Also, we prove that positive multiples of superconvex-cyclic operators are superconvex-cyclic. However, this concept is not necessarily transferred to positive integer powers of an operator. Moreover, we completely characterize superconvex-cyclic matrices whose spectra contain no real number or contain a positive real number.

复 Banach 空间上的有界线性算子T$\mathcal{X}$是超凸循环的，如果对于空间中的某个向量x ，$\mathbb{C}.Co(orb(吨,X))$是密集的。这里，co ( orb ( T , x )) 表示凸包$\{{吨}^{n}X:n\ge 0\}$. 在本文中，我们根据其伴随的点谱给出了算子的超凸循环性的必要条件。此外，我们证明了超凸循环算子的正倍数是超凸循环的。然而，这个概念不一定转移到运算符的正整数幂。此外，我们完全表征了其光谱不包含实数或包含正实数的超凸循环矩阵。