On the Wold-Type Decompositions for $n$-Tuples of Commuting Isometric Semigroups

Tudor B\^inzar, Cristian Lăzureanu

In this paper the $n$-tuples of commuting isometric semigroups on a Hilbert space and the product semigroup generated by them are considered. Properties of the right defect spaces and characterizations of the semigroups of type ``s'' are given. Also, the Wold-type decompositions with $3^n$ summands for $n$-tuples of commuting isometric semigroups are introduced. The existence and uniqueness of such decompositions are analysed and several connections with the Wold decompositions of each semigroup and their product semigroup are presented.