Properties of Unitary Quasi-Equivalence on Isometry, Co-Isometry, and Partial Isometry Operators

The present study aims to determine the properties of unitary quasi-equivalence and isometry, co-isometry and partial isometry operators. Unitary quasi-equivalence has been shown to be an equivalence relation. Similarly, unitary quasi-equivalence has been proven to preserve normality, hyponormality and binormality of operators. However, the properties of unitary quasi-equivalence and partial isometric operators have not been established. Based on the preceding results, it establishes that unitary quasi-equivalent operators preserve; isometry, co-isometry and partial isometric properties.