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Journal of Operator Theory

Volume 67, Issue 1, Winter 2012  pp. 215-236.

Algebraic pairs of isometries

Authors Jim Agler (1), Greg Knese (2), and John E. McCarthy (3)
Author institution: (1) U.C. San Diego, La Jolla, CA 92093, U.S.A.
(2) University of Alabama, Tuscaloosa, AL 35487, U.S.A.
(3) Washington University, St. Louis, MO 63130, U.S.A.

Summary:  We consider pairs of commuting isometries that are annihilated by a polynomial. We show that the polynomial must be inner toral, which is a geometric condition on its zero set. We show that cyclic pairs of commuting isometries are nearly unitarily equivalent if they are annihilated by the same minimal polynomial.

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