Some Properties and Criteria for Sub-Chaotic C0-Semigroups

Abstract

In this paper, we get a closer view to sub-chaotic C₀-semigroups. We show that if a C₀-semigroup contains a subspace-chaotic operator, then it is sub-chaotic. We prove that there are sub-chaotic C₀-semigroups that contain no subspace-chaotic operator. We also prove that if φ is a bounded and holomorphic function on the unit disk, then the multiplication C₀-semigroup generated by φ can not be sub-chaotic. Moreover, we state some criteria for a C₀-semigroup to be sub-chaotic based on the properties of the operators that made the semigroup.

Key words and phrases. chaotic C₀-semigroups, sub-chaotic C₀-semigroups, subspace-chaotic operators, semigroups.

2010 Mathematics Subject Classification. Primary 47A16, Secondary 47B37, 37B99