IUMJ

Title: Numerical invariants for commuting isometric pairs

Authors: Wei He, Yueshi Qin and Rongwei Yang

Issue: Volume 64 (2015), Issue 1, 1-19

Abstract:

The fringe operator and the defect operator are defined for commuting isometric pairs $(V_1,V_2)$. Through an analysis on their relationship, as well as the structure of the defect operator, some numerical invariants for the commuting isometric pair $(V_1,V_2)$ are obtained. A new criterion is given to classify commuting isometric pairs, namely, the congruence relation. It turns out that, in many interesting cases, the congruence relation can be determined by a pair of nonnegative integers.