SUBSPACE-HYPERCYCLIC CONDITIONAL WEIGHTED COMPOSITION OPERATORS ON Lp -SPACES

A conditional weighted composition operator T-u : L-p ( Sigma ) -> L-p(A) (1 <= p < infinity ), is defined by T-u(f) := E-A(uf omicron phi) , where phi : X -> X is a measurable transformation, u is a weight function on X and E-A is the conditional expectation operator with respect to A . In this paper, we study the subspace-hypercyclicity of T-u with respect to L-p(A) . First, we show that if phi is a periodic nonsingular transformation, then T-u is not L-p(A)-hypercyclic. The necessary conditions for the subspace-hypercyclicity of T-u are obtained when phi is non-singular and finitely non-mixing. For the sufficient conditions, the normality of phi is required. The subspace-weakly mixing and subspace-topologically mixing concepts are also studied for T-u. Finally, we give an example which is subspace-hypercyclic while is not hypercyclic.