COMPACTNESS, CYCLICITY an‎d UNICELLULARITY OF THE DIFFERENTIATION OPERATOR ON CERTAIN WEIGHTED SEQUENCE SPACES

We investigate strictly syclicity of H1 p () that is the weakly closed algebra generated by the operator of multiplication by z acting on Hp() and determine the maximal ideal space, dual space and re exivity of the algebra H1 p (). Also we give neces- sary condition for a composition operator to be bounded on Hp() when H1 p () is strictly cyclic. Next, we investigate compactness, cyclicity and unicellularity of the dierentiation operator on cer- tain weighted sequence spaces