In this note we study three operators which are canonically associated with a given linear and continuous operator between locally convex spaces. These operators are defined using the spaces of bounded sequences and null sequences. We investigate the relation between them and the original operator concerning properties, like being surjective or a homomorphism.
Our aim in this paper is to prove that every separable infinite-dimensional complex Banach space admits a topologically mixing holomorphic uniformly continuous semigroup and to characterize the mixing property for semigroups of operators. A concrete characterization of being topologically mixing for the translation semigroup on weighted spaces of functions is also given. Moreover, we prove that there exists a commutative algebra of operators containing both a chaotic operator and an operator which...
Page 1