Wandering subspace property and Wold-type decomposition for doubly commuting n-tuples of operators

El Hassan Zerouali, PhD; Department of Mathematics, University of Iowa

We introduce the notion of wandering subspace property, Beurling-type theorem and Wold-type decomposition for an operators T and for doubly commuting n-tuples T =(T_1,..., T_n) . We shown that a doubly commuting n-tuples T satisfies wandering subspace property if and only if T_i  does for every i. Applications are given in the case of Hilbert spaces of analytic functions and various recent results are extended. New results concerning Beurling-type theorem for doubly commuting n-tuples are also presented. Finally, in the case where T_i admits a Wold-type decomposition for every i, we exhibit a Wold-type decomposition for the doubly commuting tuples (T_1, ..., T_n).