Superconvex-cyclicity of operators

Abstract

A bounded linear operator T on a complex Banach space is superconvex-cyclic, if for some vector x in the space, is dense. Here, means the convex hull of . 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.