Wold-type decomposition of semigroups of isometries in Baer ⁎-rings, By Ali Bagheri-Bardi

Research

Title	Wold-type decomposition of semigroups of isometries in Baer ⁎-rings
Type	Article
Keywords	Baer ⁎-ring Wold-type decomposition Bi-isometry Isometric semigroup
Journal	BULLETIN DES SCIENCES MATHEMATIQUES
DOI	https://doi.org/10.1016/j.bulsci.2021.103049
Researchers	Ali Bagheri-Bardi (First researcher) , Gholam Hossein Esslamzadeh (Second researcher) , Mahtab Sabzevari (Third researcher)

Abstract

In this paper we continue our investigation of Wold-type decomposition in Baer ∗-rings. We obtain further information on building blocks of commuting pairs of isometries, by constructing Popovici decomposition of bi-isometries in Baer ∗-rings. Then we introduce Suciu decomposition of an Abelian isometric semigroup. Moreover, we clarify the relationship between the Wold-Slocinski’s decomposition of a given biisometry and Suciu decomposition of the semigroup induced by this bi-isometry