On existence of subspace codiskcyclicity for  C ₀ -semigroups

Abstract

This study explores the concept of subspace codiskcyclicity within the framework of C ₀ -semigroups, introducing it as a natural generalization of subspace-diskcyclicity. The work demonstrates the existence of subspace codiskcyclic C ₀ -semigroups defined over any separable Banach space of infinite dimension and proves that codiskcyclic C ₀ -semigroups form a specific subclass of subspace codiskcyclic semigroups. Furthermore, several illustrative examples are presented, constructed primarily through conditions involving non-empty relatively open and dense subsets of the underlying space.