On polynomial $n$-tuples of commuting isometries

Abstract

We extend some of the results of Agler, Knese, and McCarthy concerning pairs of commuting shifts to the case of n-tuples of commuting isometries, where n>2. Let V = (V1, . . . , Vn) be an n-tuple of commuting isometries on a Hilbert space and let Ann(V ) denote the set of all n-variable polynomials p such that p(V ) = 0. When Ann(V ) defines an affine algebraic variety of dimension 1 and V is completely non-unitary, we show that V decomposes as a direct of n-tuples (W1, . . . ,Wn) with the property that, for each i, Wi is either a shift or a scalar multiple of the identity. If V is a cyclic n-tuple of commuting shifts, then we show that V is determined by Ann(V ) up to near unitary equivalence. Talk time: 2016-07-18 05:00 PM— 2016-07-18 05:20 PM Talk location: Cupples I Room 207