DISKCYCLIC C₀-SEMIGROUPS AND DISKCYCLICITY CRITERIA

Abstract

In this article, we prove that diskcyclic C₀-semigroups exist on any infinite- dimensional Banach space. We show that a C₀-semigroup (T_t)_{t≥0} satisfies the diskcyclicity criterion if and only if any of Tt’s satisfies the diskcyclicity criterion for operators. Moreover, we show that there are diskcyclic C₀-semigroups that do not satisfy the diskcyclicity criterion. Also, we state various criteria for diskcyclicity of C₀-semigrous based on dense sets and d- dense orbits.