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

Abstract

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 2n, respectively 3n 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.