Pairs of commuting isometries, I
Volume 248 / 2019
Studia Mathematica 248 (2019), 171-189
MSC: Primary 47A05, 47A13, 47A20, 47A45, 47A65; Secondary 46E22, 46E40.
DOI: 10.4064/sm180111-14-8
Published online: 7 March 2019
Abstract
We present an explicit version of Berger, Coburn and Lebow’s classification result for pure pairs of commuting isometries in the sense of an explicit recipe for constructing pairs of commuting isometric multipliers with precise coefficients. We describe a complete set of (joint) unitary invariants and compare Berger, Coburn and Lebow’s representations with other natural analytic representations of pure pairs of commuting isometries. Finally, we study the defect operators of pairs of commuting isometries.
