The Study Of The Boundedness, Compactness And Simple Dynamical Properties Of Operators

This paper mainly contains two parts:one is the operator theory about the bound-edness, compactness, the essential norms and the differences of some operators on holo-morphic function spaces; another is linear dynamic system concerning the dynamical properties of some operators.Specially, on the first part, we investigate three-class operators:the products of differentiation and composition operators acting on Bloch-type spaces, the weighted composition operators acting from weighted Bergman spaces to mixed-norm spaces, from weighted-type spaces to Bloch-type spaces, from Hardy to weighted-type spaces; the integral-type operators acting from log-Bloch to F(p, q, s) spaces, from Hardy to Zygmund-type spaces, from F(p, q, s) to mixed-norm spaces. On the second part, we study the supercydic weighted shifts, supercydic tuples of the adjoint weighted compo-sition operators and supercydic translation Co-semigroup and hypercyclic multiples of composition operators; then we finally give the disjoint mixing composition operators on the Hardy spaces in the unit ball and the disjoint supercydic powers of weighted shifts on weighted sequence spaces.